Introduction - Ultra Fractal
Introduction
This manual contains complete documentation for Ultra Fractal 5 in printer-friendly format. All
information in this manual is also accessible from the Help menu in Ultra Fractal. You can also get
context-sensitive help in every dialog and tool window in Ultra Fractal. Click the ? button in the title
bar, and then click on a control to learn more about it.
The compiler reference is not included in this manual because it would make it unnecessary large. To
access the compiler reference, click Contents on the Help menu in Ultra Fractal. In the Writing
Formulas chapter, there is an additional Reference chapter that lists all built-in functions, operators,
keywords, and so on. Alternatively, click on a symbol in the formula editor and then press F1 or click
Help on the Help menu.
Table of Contents
1
Table of Contents
What's new?
What's new in Ultra Fractal 5?
New compiler features
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11
Getting help
Getting help
Context-sensitive help
Help for formula authors
12
13
14
Tutorials
Tutorials
Quick Start Tutorial
Creating a fractal image
Changing formula parameters
Applying a coloring algorithm
Saving your fractal
Opening your saved fractal
Learning basic skills
Learning basic skills
Learning to use Switch Mode
Using the Explore tool
Synchronizing the Julia Seed
Zooming into the image
Synchronizing the location
Adding outside coloring
Working with the gradient
Synchronizing colors and Saving the image
Working with layers
Working with layers
Coloring the new layer
Editing the gradient
Learning about layer opacity
Learning about merge modes
Adding a third layer
Transparency in the gradient
Adding control points
Learning about transformations
Learning about transformations
Using the Kaleidoscope transformation
Using 3D Mapping
Twist transformation
Mapping a sphere
Adding a frame
Zooming with multiple layers
Using the Clipping transformation
Exporting the image
Masking
Introduction to masking
Layer 2 - Waves Trap
Layer 3 - Box Trap
Fine-tuning the gradient
Layer 4 - Gaussian Integer
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19
21
22
23
24
25
27
28
29
30
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34
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38
39
40
41
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45
47
48
50
51
52
53
55
57
58
59
61
63
65
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Adding a mask layer
Editing the mask
Rendering the image
Some final thoughts
Working with animations
Working with animations
Making a zoom movie
Playing the movie
Experimenting with Animate mode
Extending the animation
Using the Timeline tool window
Adding gradient animation
Adding a new layer
Rendering the animation
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71
74
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76
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81
82
84
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About fractals
What are fractals?
Self-similarity
Julia sets
The Mandelbrot set
Fractals today
Where to start
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Workspace
Workspace overview
Working with tool windows
Tool windows overview
Layer Properties tool window
Fractal Properties tool window
Fractal Mode tool window
Statistics tool window
Color cycling tool window
Network tool window
Render to Disk tool window
Compiler Messages tool window
Options dialog
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97
99
100
101
102
103
104
105
106
107
108
Fractal windows
Fractal windows
Normal mode
Select mode
Switch mode
Opening and saving fractals
Parameter files
Copying and pasting fractals
Fractal history list
Full screen mode
Default fractal
Copyright and tweaking
Calculation details
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110
112
114
115
116
117
118
119
120
121
122
Gradients
Gradients
Gradient toolbar
123
125
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How gradients work
Editing gradients
Transparent gradients
Adjusting gradients
Opening and saving gradients
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127
129
130
131
Fractal formulas
Fractal formulas
Working with fractal formulas
Maximum iterations
Formula parameters
Explore
Eyedropper
Presets
Arbitrary precision
Public formulas
Standard fractal formulas
Embossed (Julia, Mandelbrot, Newton)
Generic Formula
Julia
Julia (Built-in)
Lambda (Julia, Mandelbrot)
Magnet 1 and 2 (Julia, Mandelbrot)
Mandelbrot
Mandelbrot (Built-in)
Newton
Nova (Julia, Mandelbrot)
Phoenix (Julia, Mandelbrot)
Pixel
Slope (Julia, Mandelbrot, Newton)
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136
138
140
142
143
144
145
147
148
149
150
151
152
153
154
155
156
157
158
159
160
Coloring algorithms
Coloring algorithms
Inside and outside
Working with coloring algorithms
Using images
Combining fractals with images
Coloring settings
Solid color
Direct coloring algorithms
Standard coloring algorithms
Basic
Binary Decomposition
Decomposition
Direct Orbit Traps
Distance Estimator
Emboss
Exponential Smoothing
Gaussian Integer
Generic Coloring (Gradient, Direct)
Gradient
Image
Lighting
None
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170
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174
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185
186
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188
4
Orbit Traps
Smooth (Mandelbrot)
Triangle Inequality Average
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Transformations
Transformations
Working with transformations
Multiple transformations
Solid color
Standard transformations
3D Mapping
Aspect Ratio
Clipping
Generic Clipping
Generic Transformation
Glass Hemisphere
Inverse
Kaleidoscope
Lake
Mirror
Ripples
Twist
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196
198
200
201
202
203
204
205
206
207
208
209
210
211
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Classes
About classes
Example 1 - Formula classes
Example 2 - Orbit trap classes
Working with classes
Standard classes
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216
218
219
Layers
Layers
How layers are merged
Working with layers
Merge modes
Transparent layers
Masks
Working with masks
Layer groups
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223
225
227
228
229
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Animation
Animation
Creating animations
Animation keys
Animate mode
Animation bar
Playing animations
Animating locations
Animating parameters
Animating gradients
Animating layers
Time settings
Editing animations
Timeline
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236
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238
239
240
242
244
246
247
249
250
5
Interpolation
Exponential interpolation
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254
Browsers
Browsers
Browser toolbar
Modal browsers
File types
Library mode
View style
Opening files and entries
Organizing your work
Finding files and entries
Formula ratings
255
257
258
259
261
262
263
264
265
266
Formula editors
Formula editors
Editing formulas
Finding text and formulas
Indenting and commenting
Templates
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269
271
272
273
Exporting and rendering
Exporting and rendering
Rendering images
Rendering animations
Rendering parameter files
Render jobs
Anti-aliasing
File formats
Resolution
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275
276
278
279
281
283
285
Network calculations
Network calculations
Network servers
Connections
Tips
Security
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287
288
289
290
Writing formulas
Writing formulas
Creating a new formula
Language basics
Formula files and entries
Sections
Expressions
Types
Constants
Variables
Parameters
Arrays
Dynamic arrays
Type compatibility
Conditionals
Loops
291
292
294
295
297
298
300
302
304
306
308
310
312
314
6
Functions and classes
Functions
Function arguments
Classes
Objects
Member visibility
Inheritance
Fields
Methods
Overriding
Constructors
Static methods
Casting
Class parameters
Extending class parameters
Parameter forwards
Importing classes
The common.ulb file
Memory management
Formulas
Writing transformations
Writing fractal formulas
Writing coloring algorithms
Writing direct coloring algorithms
Global sections
Image parameters
Random values
Symmetry
Switch feature
Providing help and hints
Tips
Debugging
Optimizations
Compatibility
Execution sequence
Invalid operations
Publishing your formulas
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320
321
323
325
327
328
329
331
333
334
336
338
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355
356
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359
360
361
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Keyboard shortcuts
General
Fractal windows
Select mode
Animations
Gradient editors
Layer Properties tool window
Fractal Properties tool window
Formula editors
Browsers
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375
Purchasing Ultra Fractal
Purchasing Ultra Fractal
Entering your license key
License information
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378
7
Support
Support
Mailing list
Acknowledgements
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380
381
8
What's new in Ultra Fractal 5?
These are the major new features in Ultra Fractal 5:
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Layer groups
With the new layer groups feature, you can organize layers in groups, which makes fractals
with many layers easier to work with. Because a layer group has a separate merge mode,
this also makes new creative merging effects possible. See Layer groups.
Select multiple layers
You can now select multiple layers and edit them together by Ctrl-clicking or Shift-clicking in
the layers list in the Fractal Properties tool window. For example, you can easily move or
delete multiple layers, apply a new fractal formula, or edit parameters that all selected layers
share. Likewise, it is also possible to select multiple transformations in the Mapping tab of
the Layer Properties tool window. This makes it much easier to work with fractals that have
many layers or transformations. See Working with layers and Working with transformations.
Image import
Import PNG, JPEG or BMP images in your fractals with the new image import feature. Simply
select a coloring algorithm that contains an image parameter, and you can select any image
on your computer to use. The coloring algorithm determines how the information from the
image is used. For example, the standard Image coloring algorithm just displays the entire
image in the fractal window. See Using images.
Formulas with classes
Formulas in Ultra Fractal can now use separate sub-formulas, which are called classes. This
allows formula authors to easily re-use common formula features in many formulas. A
formula that use classes typically enables you to select those classes yourself, which is a
very powerful way to extend the capabilities of a formula after it has been published. For
more information, see About classes. If you are a formula author and you want to
incorporate classes in your own formulas, see New compiler features.
Browser thumbnails
The browser now includes a thumbnail view for formulas, parameter sets, fractals and
gradients that gives a great overview of the available items. See View style.
Formula ratings
Ultra Fractal now contains a rating system for formulas that makes it easy to see which
formulas you should try first, and which are no longer recommended to use. See Formula
ratings.
Improved support for dual-core processors
Ultra Fractal 5 uses dual-core or multi-processor systems more efficiently. Previously, on
these systems, the fractal to calculate was split in vertical strips which made it harder to
judge the calculation. Now, the image is split in as many strips as there are cores, so it
appears to be calculated at once. If one strip finishes earlier than the other, the unfinished
strip is subdivided again. This gives an impressive speed-up with most fractals and makes it
even more worthwhile to have a dual-core system.
Improved formula compiler
Under the hood, Ultra Fractal's formula compiler uses a new and more efficient code
generator. This means that your formulas will run faster than in Ultra Fractal 4. Selecting
new formulas and opening parameter sets is faster, too.
Improved Timeline tool window
The Timeline tool window now lets you edit the properties of multiple selected ranges or keys
together, just like the way this works with layers and transformations. Previously, you could
only edit one item at a time.
Improved fractal window
The fractal window now enables you pan the fractal very precisely with the Ctrl+arrow keys.
There is a new Copy Image command on the Edit menu so you can copy the parameters and
the image of the fractal individually. Also, there is a new Gradient|Replace command on the
pop-up menu that appears if you right-click in the fractal window.
Improved formula parameters list
The list of formula parameters in the Mapping, Formula, Inside and Outside tab of the Layer
Properties tool window now enables you to horizontally resize the area reserved for
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parameter labels. See Formula parameters.
Improved Explore window
The Explore window now shows the location of the original value of the parameter that is
being explored.
Improved formula editor
The formula editor now supports editing class library files and contains an additional Check
Class Syntax command in the File menu to easily check all classes in a file for errors.
Improved Windows Vista support
Ultra Fractal 5 supports Vista's Aero user interface even better with new file open/save
dialogs, support for the Segoe UI font, and more.
Next: New compiler features
See Also
Tutorials
Writing formulas
10
New compiler features
Ultra Fractal 5 contains many compiler and formula language enhancements that make it easier to
write large and powerful formulas:
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Classes
You can now declare your own classes and use them as objects in a formula, like in Java or
C#. Classes can be declared in formula files or in separate class library files (*.ulb). Classes
can inherit from each other to create a class hierarchy. See Classes.
Functions
In classes, but also in formulas, you can declare and use functions. Functions can have an
optional return value and any number of arguments. Arguments can be of any type, and can
also be passed by reference or marked as constant. Static class functions are also supported.
See Functions.
Class parameters
Formulas can have parameters of class type. These class parameter show up as the name of
the class, with the option to select a different class that is derived from the base class of the
parameter. Such a derived class can of course implement many different options, which is a
very powerful way to expand the capabilities of a formula even after it has been published.
The parameters of the selected class appear under the name of the class and they can be
collapsed or expanded. See Class parameters.
Image parameters
Formulas, typically direct coloring algorithms, can now have image parameters. This is how
images can be imported in Ultra Fractal 5. Inside the coloring algorithm, you have full access
to the imported image data. The built-in Image class also enables you to create and
manipulate stand-alone images. See Image parameters and Image class.
Dynamic arrays
The compiler now supports dynamic arrays, which can be resized at any time, unlike the
static arrays that were available since Ultra Fractal 3. See Dynamic arrays.
New calculationPurpose predefined symbol
The new #calculationPurpose predefined symbol makes it possible to find out the purpose of
a calculation from formula code: for a fractal window, browser preview, or a disk render.
New rating setting
The new rating setting lets you rate your own formulas, so users can quickly see which of
your formulas are recommended and which are not (perhaps because you created a better
version later). See rating setting and Formula ratings.
New isInf and isNaN functions
The new isInf and isNaN functions enable you to determine whether an invalid operation
occurred on a floating-point number.
Miscellaneous
The compiler now always defines the symbol VER50. See Compiler directives.
See Also
What's new in Ultra Fractal 5?
Writing formulas
11
Getting help
Although Ultra Fractal has been carefully designed to be as easy to use as possible, you will probably
need to refer to this help file from time to time, especially while you are learning to use the program.
Click the Help button in the toolbar, click Help on the Help menu, or press F1, to get help on
the currently active document window.
The Help menu also provides links to other major chapters in the help file that you might want to
explore. The help file is divided into three major sections:
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Tutorials
If you are new to Ultra Fractal, or to its animation features, you should take some time to do
the included tutorials. This is the easiest and most enjoyable way to get to know Ultra
Fractal.
Reference chapters
After you have finished the tutorials, or any time you want to know something, the reference
chapters provide in-depth information on any of Ultra Fractal's features, such as the
workspace, fractal windows, gradients, formulas, and layers. You can access any of these
from the table of contents in the help window.
Writing formulas
In case you are interested in writing your own fractal formulas, the Writing formulas chapter
contains a short tutorial and a complete reference for the formula language used by Ultra
Fractal. See Help for formula authors for more information.
Next: Context-sensitive help
See Also
Tutorials
Workspace
Support
12
Context-sensitive help
To quickly get more information on a control or a window that you are working with, use the contextsensitive help in Ultra Fractal.
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Make sure the Fractal Mode tool window is open and just hover the mouse cursor over the
control that you want to know more about.
The Fractal Mode tool window will now show help on the control.
Often the context-sensitive help contains a link to the main help file that you can follow by pressing
the F1 key.
button in the title bar of a tool
An alternative way to get context-sensitive help is to click the
window or a dialog box, and then click the control you want to get help on. This displays the same
information in a pop-up window.
You can also get help on most formula parameters in the same way.
Next: Help for formula authors
See Also
Tool windows
Workspace
Support
13
Help for formula authors
If you are interested in writing your own formulas, you will find all information you need in the
Writing formula chapter of the help file. This part of the help file is divided into four sections:
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Language
The Language section starts with a short tutorial and then discusses the various elements of
the formula language and how to use them effectively.
Formulas
The Formulas section documents how to create fractal formulas, coloring algorithms, and
transformations, and shows how to add help and how to use various other features.
Reference
The Reference section provides complete documentation for all built-in functions, operators,
predefined symbols, compiler directives, settings, errors, and warnings.
Tips
Finally, the Tips section contains hints and guidelines that will help you to write and publish
formulas efficiently.
While you are working on a formula, you can easily access the documentation in the Reference
section.
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Place the text cursor on the function, operator, predefined symbol, or setting that you want
to know more about and press F1 or click Help on the Help menu.
This will open the help page for the symbol at the cursor position.
See Also
Writing formulas
Support
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Tutorials
To help you to get up to speed quickly with Ultra Fractal, this chapter
contains a complete set of tutorials. Starting with the basics, you will
soon learn how to create your own fractals, change the colors, add
layers, use masks, and create animations.
The tutorials are organized in such a way that beginners can follow the
steps in the main text without stopping to learn more advanced features.
Small boxes on the right contain Tips, Hints and Learn More links for
more experienced users.
The following tutorials are available:
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Quick Start Tutorial
In this first tutorial, you will learn how to create a new fractal from scratch. You will
experiment with formula parameters, add a coloring algorithm, and learn how to save and reopen fractals.
Learning basic skills
This tutorial explains the basics of working with fractals: using Switch mode, zooming, and
working with gradients to adjust colors.
Working with layers
Now that you know the basics, learn how to add new layers, work with opacity and merge
modes, and create transparent gradients.
Learning about transformations
To make things even more interesting, this tutorial shows you how to add transformations to
your fractals to create all kinds of different effects.
Masking
The Masking tutorial extends the skills that you have learned so far and shows how to use
the masking feature. Along the way, you will create a wonderful image to decorate your
Windows desktop with!
Working with animations
This final tutorial explains how to use the new animation features in Ultra Fractal 4. You will
create a zoom movie, animate parameters, including gradient control points, learn how to
use the Timeline tool window, and finally render your animation as an AVI movie.
All tutorials were written by Janet Parke (see Some final thoughts), except Working with animations.
See Also
New features
What are fractals?
Workspace
15
Creating a fractal image
When you first open Ultra Fractal, the default Mandelbrot set is shown. Since we're going to create a
new fractal from scratch, let's close this fractal.
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Click Close on the File menu to close the fractal window.
Now, the workspace is empty except for a
row of Tool Windows on the right side of
the screen. These tool windows are where
you will enter and edit the information
which creates the fractal image on your
screen. The tool windows are the
Tool windows
information center of the program and it is
advisable to keep them open at all times.
The first step in creating a new fractal is to
select a Fractal Formula which determines
the structure of the fractal with which we
will be working.
To open a new fractal window,
click New on the File menu and
select Fractal.
Fractal formulas
This opens the "Select Fractal Formula"
browser. The left pane shows three folders
(Compatibility, My Formulas, and Public)
and a file named "Standard.ufm".
There are three additional ways to access most
features and tools: Toolbar buttons, Right-click
(mouse) menus, and Keyboard shortcuts.
When you click on Standard.ufm, its
contents — a list of the formulas it
contains, appears in the right pane of the
browser window. Each formula appears as
a thumbnail that shows a preview of the
image that the formula will produce.
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Click on the Newton formula and
then on the Open button. (Note:
Make sure it's the Newton not
the "Embossed Newton" formula!)
This opens a new fractal window, loaded
with the Newton formula, which looks like
the preview in the browser window above.
The Newton formula
Next: Changing formula parameters
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Changing formula parameters
Look at the Tool Windows on the right side of your
screen and click on the Formula tab of the topmost
(Layer Properties) window.
Under the formula name at the top (in this case,
Newton) you will see settings (Drawing Method,
Periodicity Checking, Additional Precision, and Maximum
Iterations) which appear for every fractal formula. The
parameters specific to this particular formula are listed
below the dividing line (in this case: Exponent (Re),
Exponent (Im), Root (Re), Root (Im) and Bailout value).
While Guessing, the default drawing
method, is the fastest method of
rendering fractals, it often introduces
artifacts into the image. You may wish
to choose either the Multi-Pass or OnePass Linear options for accurate
rendering.
The Exponent parameter determines the number of
"arms" of the Newton fractal structure. The default value
is "3" so the fractal has three arms. Try entering
different values in the Exponent (Re) parameter.
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When you have finished experimenting, enter 4
in the Exponent (Re) parameter. Your fractal
will look like this:
Try entering negative numbers and
other values (e.g. .5, 1.2, and .0385) in
the various parameters and see how
they twist and fracture the structure.
At this stage, you may want to change the size of the
fractal window. To do this, click on the Image tab of the
second (Fractal Properties) tool window.
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Make sure the "Maintain Aspect Ratio" option is
checked and then enter a new value in the
width field.
Next: Applying a coloring algorithm
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You can customize the default fractal
window size by clicking Options on the
Options menu and selecting the
Defaults tab.
Applying a coloring algorithm
The next step in creating a fractal is to apply a Coloring
Algorithm to the fractal structure. Here's where the real
fun begins!
Coloring Algorithms
Click on the Outside tab of the Layer
Properties tool window.
The default coloring algorithm is called "None" and it simply assigns a color to each pixel. Let's load
an algorithm which will give us some more creative control over the image.
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Click the Browse button on the Outside tab which brings up the "Select Outside Coloring
Algorithm" browser.
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Click on the Standard.ucl file in the left pane
and then on the Orbit Traps algorithm in the
right pane.
Click Open to apply this algorithm to your
fractal.
The Orbit Traps Coloring Algorithm
Just as on the Formula tab, there are several settings on
the Outside coloring tab (Color Density, Transfer
Function, Solid Color, Gradient Offset, and Repeat
Gradient) which appear regardless of the algorithm
chosen. The parameters below the dividing line are
specific to the Orbit Traps algorithm.
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Click on the arrow at the right of the Transfer
Function setting and select Log from the dropdown list.
Click on the arrow at the right of the Trap
Shape parameter and select Egg from the dropdown list.
Your fractal will now look like this:
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To learn more about a particular
parameter, make sure the Fractal Mode
tool window is visible and hover over
the parameter input box with the
mouse cursor.
There are so many options available
with the Orbit Trap coloring algorithm.
It would be well worth your time to
work through them, observing what
effect each change, and each
combination of parameters, has on your
image.
You may notice, now that we have selected this combination of parameters, the black lines that
bisect each of the arms of the fractal. This is due to the precision of Ultra Fractal's calculations. We
can circumvent this effect by making a small adjustment on the Location tab.
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Click on the Location tab of the Layer Properties tool window, and enter .01 in the
Rotation Angle setting.
This rotates the fractal imperceptibly and eliminates the black lines.
Next: Saving your fractal
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Saving your fractal
This is not a very exciting fractal yet, but before we go further, let's save our work. There are various
ways to save a fractal, and we will cover them one by one in these tutorials.
This time, we will save the image within Ultra Fractal in
a text-only form called a Parameter File. This file takes
up very little space on your hard drive and can be easily
shared with other users via email and mailing lists.
Choose Save Parameters on the File menu.
Sharing parameter files with other users
With the "Save Parameter Set" browser open, you can create a parameter file which will hold all the
images we create in these tutorials. At the bottom of the browser, in the File Name field, append
the entry with tutorials.upr so that the path reads:
My Documents\Ultra Fractal 5\Parameters\tutorials.upr
(This assumes that you have installed Ultra Fractal using the default document folders. On Windows
Vista, the path will start with Documents instead of My Documents.)
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Next, in the Title field, enter Newton 1 (the title can be any length and may contain
spaces) and then click the Save button.
We will use this image again later in the tutorials so you can close the fractal window or even Ultra
Fractal itself at this time.
Next: Opening your saved fractal
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Opening your saved fractal
You can re-open the saved fractal at any time with the
parameter browser.
Choose Browse on the File menu to open the
browser.
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Browsers
Check to make sure that Parameter Files is selected on the toolbar.
Now select tutorials.upr in the left pane of the browser window and Newton 1 in the right
pane. Double-clicking on the item in the right pane will open the fractal.
Note: If you are brand new to fractals or Ultra Fractal, you might want to become more comfortable
with these beginning steps before moving along to the next tutorial. Feel free to experiment with
other fractal formulas and coloring algorithms in different combinations as you practice.
Next tutorial: Learning basic skills
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Learning basic skills
In this tutorial, we are going to learn some basic skills for working with fractals — using Switch
Mode, zooming, and working with gradients.
Let's create a new image using a different fractal formula.
Click New on the File menu, and then click Fractal.
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Select the Phoenix (Mandelbrot) formula
from the list in the right pane of the "Select
Fractal Formula" browser window.
Double-click on the name, or click Open.
If you cannot find the formula, make sure that the file
Standard.ufm is selected in the left pane first.
You should now see this image on your screen:
Next: Learning to use Switch Mode
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The Phoenix formulas
Learning to use Switch Mode
Although we could work with this image as is, let's learn about using the Switch feature to open a
corresponding Julia version of this Phoenix (Mandelbrot) fractal.
Using the Switch feature is often a good way to find
interesting fractal structure.
Click Switch Mode on the Fractal menu.
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Switch Mode
Place your mouse cursor anywhere in the active fractal window and look at the Fractal
Mode tool window on the right-hand side of your screen.
Each point in the Phoenix (Mandelbrot) set corresponds to a separate Julia-type fractal. As you move
your mouse around the fractal window, notice that a preview of that corresponding Phoenix (Julia)
image is displayed in the Fractal Mode preview window.
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When you find an image in the preview window that appeals to you, click once and a new
fractal window containing that image will open.
This window (named Fractal2) is the one with which we will be working, so you can close
the original window (Fractal1) without saving it.
Click on the Formula tab of the Layer Properties tool window and notice that this fractal
uses the Phoenix (Julia) calculation formula.
Just below the horizontal line in this same tool window are the Julia Seed parameters that you
brought to this fractal when you switched from the Phoenix (Mandelbrot) to the Phoenix (Julia)
formula.
Next: Using the Explore tool
24
Using the Explore tool
We can experiment with changing the Julia Seed values and other parameters to alter the image.
In the past, parameter values were often chosen at random because it was difficult to anticipate
what changes the values would effect. To solve this problem, Ultra Fractal has the Explore tool that
makes choosing parameter values much easier and more fun. When you click in any parameter field
that takes a numerical entry, two icons appear directly below the field.
Click the Explore button to start exploring. This opens the Explore window with a
rectangular coordinate grid.
Explore
You can also access both the
Eyedropper and Explore tools by rightclicking in any numerical parameter
field.
25
As you move the mouse cursor over the grid, the Fractal
Mode tool window shows what the fractal will look like if
the value under the cursor is selected.
You can zoom in and out to decrease or increase the
range of potential values with the Zoom In and Zoom
Out buttons, or by typing a new range value. Simply
drag the rulers to pan the window.
Click to select a new value. Experiment with the Explore
tool for a while until you are comfortable with it.
And remember that at any time, you can undo your
changes by clicking Undo or Redo on the Edit menu.
Next: Synchronizing the Julia Seed
26
You can also zoom and pan in the
Explore window by Shift-dragging and
Ctrl-dragging, like in the fractal window.
Synchronizing the Julia Seed
Because it is highly unlikely that you have chosen the exact Julia Seed values that we will be using in
this tutorial, we will need to synchronize those values before we can proceed.
The Julia Seed parameters for this tutorial image are long, complicated numbers, but you will not
need to type them in by hand.
●
Just click on them below to copy them to the Clipboard.
-0.2589852008
-0.1395348837
●
Switch to Ultra Fractal and right-click in either of the Julia Seed parameter fields on the
Formula tab of the Layer Properties tool window. In the menu that appears, click Paste
Complex Value.
Your image should now look like this:
Next: Zooming into the image
27
Zooming into the image
The most interesting fractal structure of this Phoenix (Julia) fractal exists in the red-orange-yellow
areas so let's zoom in and explore the structure there.
Click Select Mode on the Fractal menu and notice that a rectangular box appears in your
fractal window.
●
Press Enter.
The fractal now re-draws on screen filling your image with the previously selected area.
Another way to invoke the selection box is to place your
mouse cursor on an interesting part of your image. Click
and hold the left button and drag the cursor until you
have selected the area in which you wish to zoom.
Select mode
Notice that by placing your mouse cursor over different parts of the selection box, you can also
move, resize and rotate the box. The status bar at the bottom of the main Ultra Fractal window
displays helpful hints while you move the mouse cursor around.
Try these options until you have framed an interesting
section and then press Enter to zoom into this new
area. To zoom out, press Ctrl+Enter instead.
You may want to spend some time zooming in and out
to explore your fractal before we move on to the next
part of the tutorial. Don't worry about where you travel,
for we will synchronize locations in the next section.
Next: Synchronizing the location
28
Instead of pressing Enter or
Ctrl+Enter, you can also right-click in
the fractal window and click Zoom In
or Zoom Out on the menu that
appears.
Synchronizing the location
Now that you have explored a bit, let's synchronize your fractal's location with that of the tutorial
image so we can proceed together.
Click on the Location tab of the Layer Properties tool window. This time you are going to copy and
paste all the necessary parameters in one operation.
●
Click on the text below to copy it to the Clipboard.
BackgroundLocation {
location:
center=-0.3979/0.28282 magn=1102.9412
}
Now switch to Ultra Fractal and click the Paste Location button on the Location tab of the
Layer Properties tool window.
Your image should look like this:
Next: Adding outside coloring
29
Adding outside coloring
Next, let's apply a coloring algorithm to this image.
Click on the Outside tab of the Layer Properties tool window and then click the Browse
button.
●
Select the Smooth (Mandelbrot) entry in the right pane of the "Select Outside Coloring
Algorithm" browser and then click Open.
If you cannot find it, make sure Standard.ucl is selected in the left pane first.
The Smooth (Mandelbrot) coloring
algorithm
This is not very pretty but we can make some improvements by changing two of the coloring
settings.
●
Change the Transfer Function to Sqrt, which makes the image less busy...
Coloring settings
●
... and change the Color Density to 5 to add in a few more colors.
30
Next: Working with the gradient
31
Working with the gradient
So far, the only adjustments we have
made to the colors in our fractal have been
through changes we have made to the
coloring algorithm and its parameters.
Since the coloring algorithm references
colors found in the palette of the gradient,
let's open and explore the Gradient
Editor.
How gradients work
Select Gradient from the Fractal menu to bring up the gradient editor for our fractal.
You will notice that the colors in the
gradient correspond to the colors in your
image. Both the gradient editor and your
fractal contain blue, white, yellow, red, and
black areas.
Gradients
By clicking and dragging the horizontal slider on the Gradient editor to the right and left, you can
rotate the gradient, and thus the colors in your image.
You can also move individual control points
in the top 3 panels. Click on the top- and
left-most control point and drag it to the
right.
Editing gradients
Notice that you can drag it horizontally past other control points and that doing so affects the
shading between colors. Any changes made in the gradient editor are immediately reflected in your
fractal onscreen.
If you drag a control point to a position immediately adjacent to another control point, this creates a
sharp line between those two colors in the image rather than the smoother gradation that occurs
when the control points are farther apart.
32
You can also drag each control point vertically within its panel of color to change the color of that
point. Try moving the various control points up and down to see this.
Note: Unless you have experience with similar gradient editors in other graphics programs, you will
want to spend time working with the gradient editor to learn how to manipulate the control points to
make the colors you want.
While you can add, delete, move, and
adjust the control points yourself — and
you will eventually want to become very
comfortable with these skills — an easy
way to change colors is to use the
Randomize feature.
To generate a random gradient, click
Randomize Bright (or Randomize
Misty) on the Gradient menu. You can
repeatedly press their respective keyboard
shortcuts (F6 and F7) until you find a set
of colors you would like to use.
Adjusting colors and Random gradients
You can create some really interesting gradients with
the Randomize Custom editor.
Next: Synchronizing colors and Saving the image
33
Synchronizing colors and Saving the image
Now that you have become more familiar with gradients, let's synchronize the gradient of your image
with the tutorial fractal.
●
Click on the text below to copy it to the Clipboard.
Gradient-Fractal2,Background {
gradient:
title="Gradient - Fractal2, Background" smooth=yes rotation=155 index=84
color=13799050 index=247 color=16448758 index=332 color=9665827
opacity:
smooth=yes
}
Now switch to Ultra Fractal. Right-click on the gradient editor and select Paste.
Your image and gradient editor should look like this:
Before we go on, let's save the parameters for this image.
●
●
Click on the fractal image and then select Save Parameters on the File menu.
Click on tutorials.upr in the left pane of the Save Parameter Set browser and then enter
Phoenix Julia 1 in the Title field at the bottom.
34
●
Click Save.
Saving the parameters only saves the "recipe"
for the image in text form. Ultra Fractal can also
save the image in graphic form so that it can be
re-opened and edited at a later time. Let's also
save this image in this way as a .ufr file.
●
Click Save on the File menu.
By default, Ultra Fractal puts all .ufr files in its
"Fractals" folder. Since we have already named
the image, its title appears in the File Name
field and we can accept these defaults by
clicking on the Save button.
The .ufr format saves the rendered image so reopening it does not require recalculation as
parameter files do. This is very handy and timesaving for many-layered or slow-to-render
images.
See also File types.
Next tutorial: Working with layers
35
Working with layers
Note: This tutorial assumes that you have worked through the Quick Start and Basic Skills tutorials
and have saved the "Phoenix Julia 1" image from the Basic Skills tutorial.
Now that we have learned some basic skills, it is time
to explore one of Ultra Fractal's key features —
layering.
Let's open the image we created in the last tutorial.
This time we will use the .ufr file, which will open the
fully-rendered image on screen.
●
Layers
Click Open on the File menu. Locate the .ufr file — remember that we saved it in the
"Fractals" folder — click on the file name (Phoenix Julia 1.ufr) and click Open.
Now look at the Fractal Properties tool window. Click on the Layers tab and notice that there is a
tiny copy of the image in a layer named Background.
To add a new layer, simply click the Add
Layer button on the Layers tab.
If you click and hold down the Add
Layer button, a menu with predefined
layers appears. Click a predefined layer
to add it, or click Define to customize
the menu.
Now you will see two layers — your original, still
labeled "Background", and a new, identical layer
labeled "Layer 1".
Next: Coloring the new layer
36
Coloring the new layer
Let's apply a different coloring algorithm to this new layer.
Click on the Outside tab of the Layer Properties tool window and then click the Browse
button.
●
Select the Triangle Inequality Average
coloring from the browser's right pane and click
Open.
You can immediately see the new coloring applied to the
fractal. These colors are OK, but let's take this
opportunity to learn more about gradients.
●
The Triangle Inequality Average
coloring algorithm
First, open the gradient editor by selecting Gradient from the Fractal menu.
We could adjust the control points on this gradient, or generate a random gradient as we learned in
the Basic Skills tutorial, but we can also load a pre-saved gradient.
●
To load a pre-saved gradient, select Replace from the File menu.
The "Select Gradient" browser shows the pre-saved
gradient files that come with Ultra Fractal and any
gradients you have saved or imported.
Opening and saving gradients
Click on the Standard.ugr gradient file in the
left pane of the browser window and Grayscale
in the right pane. Click Open.
The pre-saved Grayscale gradient has now been loaded into the gradient editor and the active layer
of your fractal.
●
Next: Editing the gradient
37
Editing the gradient
Before we edit the gradient, go to the Outside tab of
the Layer Properties tool window.
Editing gradients
Change the Color Density setting to 1 and the
Transfer Function setting to Linear.
Now, looking again at the gradient editor, you will notice that there are only two sets of control
points. Those in the left-most set are all at the bottom of their respective color panels — creating
black, while those in the middle of the gradient editor are at the top of their panels — creating white.
●
●
Let's move the control points around until we increase the contrast between the white and
black areas. As you drag the control points, be sure to keep them pulled all the way down
(for black) or all the way up (for white) in their color panels to prevent introducing color into
the gradient.
After you have experimented with moving the control points, let's synchronize their positions.
●
A nice contrast can be found with the set of white control points at Position setting 130 and
the black control points at Position setting 185. You may either drag the points to these
locations, or click on the respective points and type their positions into the Position setting.
Your image and gradient should now look like this:
Next: Learning about layer opacity
38
Learning about layer opacity
If you will look again at the Layers tab of the Fractal
Properties tool window, you will see both your layers
and their tiny thumbnails listed.
Working with layers
But when you look at your image, you only see the top, grayscale layer. This is because the top layer
is 100% visible in "Normal" merge mode, which means that you will not see any layers underneath
it.
To check that the other layer is still really there, click the Visible icon on the Layer 1 layer.
This toggles this layer's visibility off and on. When the visibility is off, you will see the layer(s)
underneath. When it is on, you will see the active layer.
Having multiple layers in our image is useless, though, unless we can see more than one at a time.
There are many ways to do this, so let's work through them one at a time.
At the top of the Layers tab there are two controls. The one on the left is the Merge Mode setting
(which currently says "Normal") and to its right is a horizontal slider (currently all the way to the
right at 100%).
●
Make sure the top layer of your fractal (Layer 1) is visible again. With the top layer
highlighted in the layer list, click and drag the Opacity slider slowly to the left and watch
what happens to your fractal.
As the top layer becomes more transparent, the bottom (Background) layer begins to show through.
When the Opacity slider is all the way to the left, at 0%, the top layer is no longer visible at all.
Next: Learning about merge modes
39
Learning about merge modes
Another way to view more than one layer at a time is to
change the way the layers interact with the Merge
mode setting. This setting determines how each pixel
combines with the pixel(s) directly underneath it in other
layers.
●
Make sure the opacity of the top layer is set at
100% and then click on Normal in the Merge
mode drop-down box. Select the next option —
Multiply.
Notice that the colors from the Background layer are
now visible (although they appear darker) along with the
textures of Layer 1.
●
●
●
●
How layers are merged
Merge modes
Use the down arrow key on your keyboard to cycle through the list of merge modes.
Remember that you can also change the opacity setting with any of the merge modes.
You can also reverse the order of the layers by clicking on the title of one and dragging it up
or down in the list. After reversing their order, try changing the merge modes of the
Background (top) layer.
When you are finished exploring all the options, make sure the Background layer is on the
bottom. Layer 1 should be on top with the Hard Light merge mode selected. Also make
sure that both layers are set at 100% opacity.
Before we go on to the next step, save this image — either by saving the parameter file, or
the fractal (as a .ufr). Keep the image name (Phoenix Julia 1) the same.
Next: Adding a third layer
40
Adding a third layer
Let's explore another way to work with layers.
Click on the Layer 1 layer and then on the Add Layer button.
Note that a new layer appears at the top of the list and that it is identical to Layer 1 in every respect
except for its name, which is Layer 2.
These layer names start to get confusing, so let's give
them more descriptive names.
●
●
●
Right-click on the Background layer and
choose Rename from the right-click menu.
Type Coloring as its new name and press
Enter.
Rename the middle (Layer 1) layer Texture.
Rename the top layer Web.
The Texture and Web layers still look the same, they
just have different names.
With the Web layer highlighted, go to the
Outside tab of the Layer Properties tool
window and click on the Browse button.
One method of naming layers is to use
the coloring algorithm applied to that
layer, except that can get confusing if
you use the same algorithm on more
than one layer. Another idea is to give
them functional names that relate to
what effects they contribute to the
overall image.
Note: There is no right or wrong way to
name layers and indeed you may never
want to rename them at all. You will
eventually develop a system that is
meaningful to you.
Select the Orbit Traps coloring algorithm from
the right pane and click Open.
This creates a soft, gentle effect that you might be interested in pursuing at another time, so let's
make a duplicate of the whole fractal and save it for later.
●
●
Select Duplicate from the File menu.
Notice that the name of the duplicate is Copy of Phoenix Julia 1. Save the duplicate image either as a
parameter or fractal file. You can choose to keep this name, or give it another, as you wish.
Next: Transparency in the gradient
41
Transparency in the gradient
Let's go back to the Orbit Trap coloring on the top (Web) layer and change some settings.
●
Enter 5 in the Color Density setting, and select rectangle as the Trap Shape parameter.
We need to work with the gradient for this layer to better see the trap shapes, so open the gradient
editor by selecting Gradient from the Fractal menu.
●
Click and drag the set of white control points to the left to position 85. Click and drag the
set of black control points to position 86.
This creates a sharp line between the white and black areas of your fractal.
Now let's open up a new part of the gradient editor — the Opacity bar — by clicking on the
little down arrow next to the word Opacity, just above the rotation slider. This opens a
fourth horizontal band of color that looks right now very much like the other three.
Just as the opacity setting on the Layers tab controls
the transparency of the entire layer, the opacity bar in
the gradient editor allows us to assign different
transparencies to the individual colors in our gradient.
Transparent gradients
●
By default, the opacity bar is empty. Let's link it to the color bars so they both contain the same
control points.
Click Link Color and Opacity on the Gradient menu.
●
●
Click on the set of white control points — they are the ones at the tops of their respective
color bands.
Click and hold that same highlighted control point in the Opacity channel and drag it all the
way to the bottom, keeping its position at 85.
Note: This can be a tricky maneuver with all the control points so close together. You can also enter
the new opacity value (0) manually. Remember you can always Undo an unwanted change.
Your fractal and gradient should now look like this:
42
Note that the areas that were previously white are now completely transparent, allowing the Coloring
and Texture layers to show through.
Next: Adding control points
43
Adding control points
Let's add a couple of more control points to our gradient to
refine our web-like structure.
Right-click anywhere in the gradient editor and select
Insert from the right-click menu.
●
●
●
With the insert mouse pointer, click to the right of the
set of black control points in any one of the horizontal
color bands.
Change the Red, Green, and Blue settings each to 0.
Change the Position setting to 115 and the Opacity
setting to 255.
This creates a black control point with 100% opacity.
●
While you are working with the
gradient, try to show and hide the
various layers once in a while to see
what is going on.
If you hide the Texture and Coloring
layers to make only the Web layer
visible, you can easily see and edit the
transparent areas that the gradient
creates.
Add another control point with these settings:
❍
Red, Green, and Blue set to 255
❍
Position set to 116
❍
Opacity set to 0
This creates a 4th set of control points — this time white, with 100% transparency.
●
Save this image (either as a parameter or fractal file) as Phoenix Julia 2.
Try playing with the control points of
the Web layer gradient and watch what
happens in your image. Change their
transparencies, move them around,
give one or more of them color. And
periodically, while you are playing
around, try different merge modes and
opacity settings on the Layers tab of
the Fractal Properties tool window.
You can also experiment with changing
the order of layers in the list to see how
this affects the overall image.
Next tutorial: Learning about transformations
44
Learning about transformations
Note: This tutorial assumes that you have completed the Quick Start, Basic Skills, and Layers
tutorials. This includes: opening a new fractal, selecting fractal formulas and coloring algorithms,
opening and working with the gradient editor, adding layers and changing merge modes.
In this tutorial we are going to use the Newton 1 image we created in the Quick Start tutorial.
●
Locate and open its parameter set. (Hint: You will want to Browse the tutorials.upr file.)
We are going to make a square image this time, so click on the Image tab of the Fractal Properties
tool window.
Uncheck the Maintain aspect ratio box and change the Width setting to match the
Height setting.
In Ultra Fractal, transformations are formulas that
apply special effects to the fractal. They are selected and
applied to a layer on the Mapping tab of the Layer
Properties tool window.
Transformations
●
To add a transformation, switch to the Mapping tab and click the Add button.
Select the Lake transformation in the
Standard.uxf file of the "Select
Transformation" browser. This applies a rippled
The Lake transformation
water effect to this layer of your fractal.
You will notice that the first two parameters for this transformation are Water level (Re): and Water
level (Im):. This means that the coordinates that provide the location of the water level are a
complex number. The default setting is 0, 0 and on our fractal, this places the water level at the
middle of the fractal.
●
To change this, right-click in one of the Water level parameter fields and select
Eyedropper from the menu that appears.
Now move your mouse cursor over the fractal image. You will notice that the cursor has become an
eyedropper with crosshairs at the tip. The Fractal Mode tool window shows what the fractal would
look like with the value currently under the mouse cursor.
●
Choose a new placement for the water level with the crosshairs and click the left mouse
button.
The fractal immediately redraws, placing the water level at these new coordinates. Try different
locations.
●
When you are finished playing with this nifty tool, Check the Use screen center option on
the Mapping tab.
This will override any Water level settings and return the level to the center of your fractal so that
your image looks like this:
45
Next: Using the Kaleidoscope transformation
46
Using the Kaleidoscope transformation
Before we add another layer, let's rename this layer in the Layers tab of the Fractal Properties
tool window.
●
●
Rename the current layer Lake.
Add another layer and rename it Sky.
Go ahead and leave the Normal merge mode and 100% opacity settings as they are. This means
we will not be seeing the bottom layer for a bit.
On the Mapping tab of the Layer Properties tool window, delete the Lake transform by
clicking the Delete button.
The layer again looks like our Newton 1 image from the Quick Start tutorial.
●
Add a new transformation — the Kaleidoscope transformation in Standard.uxf.
We are going to keep the default settings for this layer, but this transformation has a lot of
interesting effects you may want to pursue at a later time.
The Kaleidoscope Transformation
Next: Using 3D Mapping
47
Using 3D Mapping
It is possible to add more than one transformation to the
same fractal layer, so let's do just that.
●
Add the 3D Mapping transformation on top of
Kaleidoscope.
The idea of the 3D Mapping transformation is to map the
fractal layer onto a three-dimensional surface. Let's first
use the default, Plane shape.
Multiple transformations
The 3D Mapping transformation
As you can see, our kaleidoscopic flower shape has been mapped onto the lower half of the fractal
and the top half of the image is now black. This gives the effect of a floor extending toward the
horizon.
We can make this mapping shift to the top half of the image, to become more of a sky-effect, by
changing one of the transformation parameters. It is not immediately clear which of the parameters
effects this change, so now is a good time to learn another way to get Help.
●
Make sure the Fractal Mode tool window is
visible, and move the mouse cursor over the
different parameters for the 3D Mapping
transformation.
The tool window will display a help text for the
parameter currently under the mouse cursor.
In this case, a little investigation tells us that the
parameter we need to change in order to make our
fractal appear in the "sky" is the Y Translation
parameter. It is currently set to -0.5.
●
If we change that to 0.5, the fractal moves into
the upper half of the image.
You can also click on the ? button in the
title bar (in the upper right corner) of
the Layer Properties tool window and
place your cursor over any parameter
field or transformation setting. When
you left-click, a helpful hint for that
particular parameter or setting will pop
up on the screen.
Conscientious formula writers will
provide helpful hints for their formulas'
parameters.
48
Now... what is this big black area doing in our image?
Some transformations, like Lake and Kaleidoscope warp
the fractal but still fill the entire image.
Solid color in transformations
Others, like the 3D Mapping transform, map the fractal onto an object or create a mask that does
not fill the entire image. The leftover area that is not fractal is filled with a solid color, which is
designated on the Mapping tab.
●
To see this, click on the black area next to the Solid Color setting. This opens a Select
Color dialog.
To change the solid color from the default Black to another color, adjust the sliders. You will see the
changes immediately on your image. But what we really want to do in this image is to make the
black area transparent.
●
Drag the Opacity slider all the way to the left.
Now we can see both the Lake effect from the bottom layer and the Kaleidoscopic flower in the sky
plane of our top layer.
●
Click OK to close the "Select Color" dialog.
Next: Twist transformation
49
Twist transformation
Add a third layer and rename it Sphere.
Delete the Kaleidoscope and 3D Mapping transformations from the Mapping tab.
●
Add a new transformation — Twist.
This is a fun transform, because you can use the
eyedropper to select the center of the twist. Remember
to right-click in one of the Twist Center parameters to
select and activate the Eyedropper, or click the
eyedropper button that pops up when you click on the
The Twist transformation
parameter.
●
●
The Strength and Decay Factor parameters affect the tightness and shape of the spiral. Try
making them smaller and larger. Try using a negative number in the Strength parameter.
Remember that you can use the Explore tool as well.
When you are done playing with these parameters, click on the complex number below to copy it to
the Clipboard.
-0.65 / -0.18125
●
●
Paste it into the Twist Center parameter by selecting Paste Complex Value on the rightclick menu.
Enter 4 in the Strength setting and 10 as the Decay Factor.
Next: Mapping a sphere
50
Mapping a sphere
Let's add another mapping transformation to this layer.
●
●
●
Load 3D Mapping again and this time select
the Sphere shape.
First, let's change the solid color opacity to 0.
Next, to center the sphere in the image, change
the Y Translation setting to 0.
You can resize the list of
transformations by clicking on the
dividing line above the parameters and
dragging downwards.
The help hint for the Z Translation setting says that increasing the value will move the sphere
farther away (thus making it smaller).
●
Let's change that setting to 2.5.
Now the sphere is positioned just below the Kaleidoscopic flower.
Transformations are applied in a
particular order, starting with the
bottom one on the list and working
upward. So it matters, sometimes, in
which order they are placed in the list.
For fun, reverse the order of the Twist
and 3D Mapping (Sphere) transforms by
dragging one above or below the other.
As you can see, the sphere is now
mapped before Twist is applied resulting
in an unusual effect.
Next: Adding a frame
51
Adding a frame
In this last part of this tutorial, we are going to add a simple frame to our image. One way to do this
is to create a solid color layer (which will become the frame) and then clip out a transparent area in
the middle of the image through which the other layers below may be seen.
●
●
Add a new, fourth layer, name it Frame, and remove the transformations on the Mapping
tab.
Click on the Formula tab of the Layer Properties tool window and replace the current
(Newton) formula with the Mandelbrot formula in Standard.ufm.
Before we go on, notice the black area on the inside of
the Mandelbrot figure. Up until now, in the images with
which we have worked, we have only dealt with
"Outside" points and "Outside coloring." In this layer, we
are going to work with the Inside points.
The coloring of inside points is controlled on the Inside
tab of the Layer Properties tool window. Switch to the
Inside tab and notice the Transfer Function setting.
When the Transfer Function is set to None, the coloring
algorithm is ignored and the Solid Color setting takes
effect.
Inside and Outside areas
Solid Color
To see how this works, let's change the solid color to something other than black.
●
Click on the Solid Color swatch on the Inside tab. Click and drag the Luminance slider to
255, and note that the inside of the Mandelbrot figure becomes solid white.
Next: Zooming with multiple layers
52
Zooming with multiple layers
We will use the solid white area in the center of the
Frame layer as the basis of our frame so we are going
to zoom into it without changing the location of any of
the layers below.
To do this, click on the Layers tab of the Fractal
Properties tool window.
Locate the Editable icon on the top (Frame)
layer. While holding down the Shift key, click
on this icon.
By holding down Shift while clicking on
the Visible, Editable, or Transparent
icons, you toggle all other layers
instead. This also works with the Enable
icon on the list of transformations on the
Mapping tab.
This disables the editability of all the other layers.
Having the Editable icon enabled for just this layer means that any location changes we make will
only affect this layer. The layers for which the Editable icon is grayed out will remain unchanged.
●
Now choose Select Mode from the Fractal menu to activate the selection box. Click and
drag on one of the sides to make the selection box small enough to fit entirely into the solid
white area, something like this:
53
●
Select Zoom In from the Fractal menu.
Your top layer should now be solid white. You can verify this by looking at your Layers list.
And, by Shift-clicking the Visible icon on each layer in the list, you can see that none of
the other layers has changed location.
Note: If something went awry, you can always use the Undo option on the Edit menu to recover.
Next: Using the Clipping transform
54
Using the Clipping transformation
The last transformation we will explore in this tutorial is
Clipping. This handy transform has many uses, but we
will use it in this image to clip out the inside of our
frame.
The Clipping transformation
Add the Clipping transformation to the Frame
layer.
First, we will center the frame on the screen.
●
●
●
Switch to the Location tab, right-click on one of the Center settings and select Copy
Complex Value.
Then switch to the Mapping tab and right-click on either of the Clipping Center
parameters and select Paste Complex Value from the right-click menu.
This ensures that the clipping center is set to the center of the screen.
●
On the Mapping tab, find the Region parameter and change it to inside — because we will
be clipping out the inside area.
The image will become black — the designated solid color for this transformation.
●
To select our frame width, right-click in one of the Right Edge parameter fields and select
Eyedropper from the menu. Place the eyedropper (your mouse cursor) near the right edge
of the image and left-click.
You can repeat this until your frame is the desired width. You should now have a white frame with a
black square inside.
●
Click on the Solid Color swatch on the Mapping tab and change the Opacity to 0.
You should now be able to see the underneath layers surrounded by a white frame. As one last
finishing touch, let's change the color of the frame to coordinate with the fractal by using the
eyedropper tool.
●
Switch to the Inside tab and right-click on the white-colored Solid Color swatch. Select
Eyedropper.
As you move the eyedropper over the image, the color underneath the center of the crosshairs is
shown in the Solid Color swatch.
●
When you have found a color you like, left-click.
This changes the white frame to a color that coordinates with your image. With the exception that
your frame may be a different color and/or width, your image should now look like this:
55
Next: Exporting the image
56
Exporting the image
Let's save this image in both parameter and fractal file form. Save it with the name Newton World.
We can also export images to graphic file formats that
can be used outside of Ultra Fractal. This is useful when
you want to print an image or post it on the web.
●
To export the image, click Export Image on
the File menu.
Exporting
By default, the image will be saved in Ultra Fractals'
Export folder with the name we have given it (Newton
World).
●
●
File Formats
Ultra Fractal supports several file formats so
let's select JPEG from the Save as type: drop
down list.
When you click Save, Ultra Fractal will ask you to select the export quality for the JPEG
image. Move the slider to 95%. This will allow for some compression (which makes the file
smaller) without too much loss of quality. Click OK.
Now you may open the image up in another graphics program, email it to a friend, or post it on a
web page.
Note: All exported and rendered images made with an evaluation copy of Ultra Fractal will be
marked with Evaluation Copy text. Please purchase your copy of the software!
Next tutorial: Masking
57
Introduction to Masking
One of the most exciting features of Ultra Fractal is the ability to create layers that serve as masks
for other layers. These layers contain areas of both transparency and opacity that allow only
designated areas of the linked layer to be visible. This ability opens up a whole range of artistic
possibilities that have never before been available in fractal software.
Before we get to the actual masking concept, though, let's create a new image using some of the
skills we have learned thus far.
●
●
Create a New Fractal using the Julia formula.
Click on the complex number below to copy it to the Clipboard.
-0.815 / 0.235
Right-click on the Julia Seed parameter on the Formula tab and click Paste Complex
Value.
●
Apply the Triangle Inequality Average coloring algorithm on the Outside tab.
Note that the Julia calculation formula and the Triangle
Inequality Average coloring algorithm each have a
Bailout parameter. This tells Ultra Fractal how many
times to iterate the formula before designating a point
Inside and outside points
"inside" or "outside."
●
In this case, the bailout setting for the Julia formula is 4 and the bailout for the Triangle Inequality
Average coloring is 1e20 — a much higher number (100 sextillion) that, for our purposes,
approximates infinity.
●
●
This coloring algorithm is intended to work best when the formula and coloring have
matching bailout values, so let's change the Bailout value on the Formula tab to 1e20 to
match the higher value on the Outside tab.
Next, open the Gradient Editor and rotate the rotation slider to the left until the Rotation
setting is -137.
Our first layer should look like this:
●
In this image, we are going to name our layers by the coloring algorithm used, so Rename
this layer to TIA.
Next: Layer 2 - Waves Trap
58
Layer 2 - Waves Trap
●
●
●
●
●
Add a new layer and Rename it Waves Trap.
Replace the current Outside coloring with Orbit Traps and make the following setting and
parameter changes:
Change the Transfer Function to Log
Uncheck the Repeat Gradient box
Change the Trap Shape to Waves
Now, open the gradient editor to edit the gradient for this layer to meet the following conditions:
●
●
●
●
Three control points — You can delete unneeded control points with the right-click menu
Position the first (left-most) control point at 0 and color it White
Position the second control point at 35 and color it Black
Position the third control point at 399, also colored Black
Your image and gradient editor should look like this:
●
Change the Merge mode on the Layers tab of
the Fractal Properties tool window to Screen.
The TIA layer now shows through the white filaments of
the wave trap.
59
Merge modes
Next: Layer 3 - Box Trap
60
Layer 3 - Box Trap
Let's do some fun things with gradient transparency.
●
●
Add a new layer and Rename it Box Trap.
Change the Trap Shape parameter on the
Outside tab to Box.
Transparent gradients
Switch back to the Layers tab and Shift-click the Visibility icon on the Box Trap layer to
toggle the other two layers off. This will help us to better see what we are doing with this
layer.
Since the Waves trap tendrils are white, let's make the Box trap shape a different color.
●
In the gradient editor, edit the set of white control points so that the Red, Green, and Blue
settings are 145, 147, and 253, respectively.
Select Link Color and Opacity from the Gradient menu. This allows us to move and edit
the color and opacity curves simultaneously. Also, make sure that the opacity part of the
gradient editor is visible — click the small opacity button to expand it if necessary.
●
●
Insert a new point in the gradient editor. Set the Opacity of this control point to 0. Also
set the Red, Green, and Blue settings to 0 to create Black.
Now Insert another control point to the right of that one. Change its Opacity to 255 and
make it black, also. Click and drag this point until it is positioned just to the right of the
transparent point.
Although the exact location of the transparent areas may differ slightly, your image and gradient
editor will look similar to this:
61
The gray and white checkerboard on both the gradient and the fractal layer indicates areas of
transparency.
●
To see how this works, change the Merge Mode of the Box Trap layer to Normal and then
Shift-Click its Visible icon to toggle the other layers on and off.
Notice that the underneath layers are only visible in the checkerboarded area of the top layer.
Next: Fine-tuning the gradient
62
Fine-tuning the gradient
We now have five control points in our gradient. The two
on the left (bluish-purple and black) control the box trap
structure in the center of our image. The next two, one
transparent and one opaque, create a sharp scalloped
line outside of the box trap structure. And the fifth
(black/opaque) control point is positioned at the far right
of the gradient editor.
You can resize the gradient editor to
make it easier to edit control points that
are closely spaced together.
Insert a new control point somewhere between the second and third points. Color it black,
with 0 opacity.
●
●
●
●
Click and drag this new point slowly to the left and watch how the spaces inside the box
trap structure become transparent. Place this point just to the right of the second (black)
control point.
Hold down the Ctrl key and click on the second
(black/opaque) and third (black/transparent)
control points. This selects both control points,
Keyboard shortcuts for gradient editors
allowing them to be moved together.
Since we want to maintain their color and opacity values as they are moved, hold the Shift
key down and drag the two points left and right. Notice that moving the two points to the
right makes the shapes fatter, and to the left, thinner.
Find a location for these two points that appeals to you, then click elsewhere on the
gradient to deselect them.
Now, let's work more with the next two control points — those that control the outer, scalloped edge.
We are going to add a little sculpted edge to the scalloped frame.
●
●
●
●
●
To the right of the fourth (black/transparent)
and fifth (black/opaque) points, Insert a new
control point. Make it white and set its Opacity
Editing gradients
to 255. Move it close to the fourth and fifth
points.
Insert one more point to the right of the white one. Make this one black and fully opaque,
also. Move it close to the white point.
Experiment with the spacing of these two newest points -- dragging them a little to the right
and left to see how they affect the width of the scalloped edging. Find an arrangement that
appeals to you.
Now select and move the grouping of our four scalloped edge control points, maintaining
their spacing and coloring. Ctrl-click each to select and add them to the group. Hold the
Shift key as you drag them right or left to position the edging. Find a position that appeals
to you.
Shift-click this layer's Visible icon to toggle all the layers on.
Your image should look something like this:
63
Save your image as a parameter and/or a fractal file. Name it Masked Julia.
Next: Layer 4 - Gaussian Integer
64
Layer 4 - Gaussian Integer
We are almost ready to learn about masking, but first we need to add one more layer.
In the Layers tab of the Fractal Properties tool window, Add a new layer and Rename it
Gaussian Integer.
●
Replace the current Outside coloring with
Gaussian Integer.
No changes to the parameters are needed but we do
need to work with the gradient a bit. Many of the control
points we added in the last layer are not needed here.
We want to keep the first two control points on the left
side of the gradient. They are, respectively, bluishpurple/opaque and black/opaque.
The Gaussian Integer coloring algorithm
We will not need the third (black/transparent) point, so click on it, right-click in the
gradient editor, and select Delete from the menu.
We also want to keep the black/opaque point at the very
right of the gradient editor. But we can delete the group
of four points that control the scalloped frame.
●
●
Most right-click commands are also
available in the Gradient pull-down
menu and on the toolbar.
Ctrl-click to select each of them, right-click in
the gradient editor and select Delete from the
menu.
Now, to make the little dots in the image a little bigger, click and drag the second (black)
control point to the right, somewhere around the Position of 40.
Next: Adding a mask layer
65
Adding a mask layer
We now have little bluish-purple dots covering the entire image. We could make the black areas
transparent or change the merge mode to allow us to see the underneath layers, but wouldn't it be
great if we could have the dots appear only in the solid black areas outside the scalloped frame?
Editing the transparency of the gradient will not
accomplish this, nor will changing the merge mode or
layer transparency. What we need to do is create a
Mask for this layer that has the same shape as the
scalloped edge in the Box Trap layer.
Masks
Go to the Layers tab of the Fractal Properties tool window.
Click on the Box Trap layer and then click the Add layer button.
This adds the new layer between the Box Trap and Gaussian Integer layer.
●
Rename this layer Mask.
But it is not a mask layer yet until we associate it with the Gaussian Integer layer.
To turn the layer into a mask, click the Use as Mask button.
Look at your image and notice how the dots no longer appear inside the scalloped frame (except on
the box trap structure inside, which we will fix in a minute).
66
Also notice on the layer list that the Gaussian Integer and Mask layers now share a Visible icon. If
you shift-click this icon to toggle the other layers off, you will clearly see which areas are visible
and which are made transparent by the mask layer.
Next: Editing the mask
67
Editing the mask
Now let's edit the mask itself. To make this easier,
we need to make the mask layer visible on its own
temporarily.
Click on the Mask layer and then on the
Show Mask Only button.
Working with masks
Masks are always shown in black and white — never any colors. White represents the areas that are
transparent and black represents the opaque, masked areas.
Looking at our Mask layer and its gradient, can you see what we need to do in order to clear out the
center of the scalloped frame? (Make sure the opacity part of the gradient is visible before you
continue.)
Since the first two control points on the left are white, and they correspond with the inner structure
on the Box Trap layer, they are the ones we need to edit.
●
●
Drag the first two points downward, making them black, so that the mask looks like this:
Click the Show Mask Only button again
(so it is no longer down) and make sure
that the bottom three layers are now
visible.
You should see the rippling of the TIA layer, the
white tendrils of the Wave Trap layer, the bluishpurple structure of the Box Trap layer, and the dots
of the Gaussian Integer layer — masked to only
appear outside of the scalloped edge.
68
When working with masks, you will often
toggle the Show Mask Only button on and
off to alternatively work on the mask and
judge its effect on the final image.
What is missing, though, is the little white edging we created around the scalloped frame.
With all the layers still visible, click again on the Mask layer. There are still some control points on
its gradient that are preventing us from seeing the white edging.
Locate the two white points indicated in the screenshot below:
●
●
Click on the first (left) of these two points and delete it.
Click on the second point and drag it downward (making it black) and to the right, just next
to the white control point.
You should now see the white edging from the Box Trap layer along the scalloped frame.
69
Next: Rendering the image
70
Rendering the image
Now that our image is complete, save it again, in either the parameter or fractal file format you
chose earlier.
There is one other method of saving images that you will
want to use on occasion. If you want to make a larger
render than is practical onscreen or render the bestquality image, you will want to use Ultra Fractal's
Render to Disk feature.
Rendering images
For fun, let's make a render of this image that you can use as your desktop wallpaper.
To start the disk render, select Render to Disk from the Fractal menu.
In the Destination File field, Ultra Fractal will suggest a file name for the rendered image. Write it
down so you will know where the image is going to be saved.
●
●
Make sure that Bitmap image (*.bmp) is the selected File Type.
In the Size field, enter the Width and Height of your Windows desktop (for instance, 1024
and 768).
If you do not know your desktop setting, minimize Ultra Fractal and right-click on your Windows
desktop. Select Properties. Click on the Settings tab and look for the Screen resolution that is
selected.
In most cases, the Anti-aliasing setting of Normal is
sufficient.
The difference between an exported and an anti-aliased
render of this image is demonstrated in the two
examples below:
71
Anti-aliasing
Exported
Rendered to disk with anti-aliasing
72
Notice how much smoother and cleaner the second image is. Fine filaments, like the white wave
tendrils, are much nicer when the image is anti-aliased.
Note: Remember that all exported and rendered images made with an evaluation copy of Ultra
Fractal will be marked with Evaluation Copy text. Please purchase your copy of the software!
To make sure the fine dots and filaments are rendered correctly, enable the Force Linear
drawing method option. This forces Ultra Fractal to use the One-pass Linear drawing
method on all layers which produces more accurate results than the default Guessing
drawing method.
●
You can accept all the other default settings in the Render to Disk tool window so click OK
to start the render.
As the render starts, you will notice that the Render to
Disk tool window on the right side of your screen opens.
This window monitors and shows the progress of the
render.
Managing render jobs
●
●
When the render is complete, right-click on the Windows desktop and select Properties. On
the Desktop tab, click the Browse button and locate the rendered image. (Usually, it will
have been saved as My Documents\Masked Julia.bmp). Click OK.
Next: Some final thoughts
73
Some final thoughts
These tutorials are intended to introduce many of the features of Ultra Fractal. They, by no means,
cover all of the program's capabilities. The creative possibilities, particularly in the use of masking
layers, are endless.
You are encouraged to work through the tutorials more than once, to become familiar with the
program's user interface and the various concepts and skills introduced in them. As you become
more comfortable, try experimenting with different parameter values and settings; move layers
around and alter their gradients; use different merge modes and opacities. If you will take the time,
at first, to explore what is possible using just these tutorial images, you will have a much better idea
of how to achieve the effects you desire when you strike out on your own.
And lastly, many people are loathe to read Help files, often because the software is poorly
documented and the Help is not very helpful. Ultra Fractal is quite different in this regard and you
will find its extensive Help files to be easy to read and full of information.
All tutorials except Working with animations were written by Janet Parke. Living in Tennessee, USA,
Janet is a widely respected fractal artist and also a ballet teacher. She has been working with Ultra
Fractal since the first beta releases in 1998. For some examples of her work, visit her online galleries
at www.parkenet.org/jp/galleries.html. You will also find a lot of Ultra Fractal resources and
information on her web site.
74
Working with animations
Note: You will only be able to follow the steps in this tutorial if you are using Ultra Fractal Animation
Edition. In addition, if you are not already familiar with Ultra Fractal, you should work through the
Quick Start, Basic Skills, and Working with layers tutorials first.
One of the major features in Ultra Fractal is the ability to turn any fractal into an animation and
make a movie out of it. In this tutorial, we will start with a simple fractal and gradually turn it into a
more and more complex animation using the various new animation features. Finally, we will render
it as a movie.
First, close any open fractal windows to begin with an empty workspace.
Click New on the File menu, and then click Fractal. In the Select Fractal Formula browser,
select Phoenix (Julia) in Standard.ufm and click Open.
This opens a new fractal window with the Phoenix (Julia) fractal. Let's change the Julia Seed
parameter of this fractal formula to make it a little more interesting.
●
●
Click on the complex number below to copy it to the Clipboard.
-0.41/-0.53
Right-click on the Julia Seed parameter on the Formula tab and click Paste Complex
Value. This should fill the input boxes with -0.41 and -0.53, respectively.
Go to the Outside tab, and click the Browse button to choose another coloring algorithm.
Select Orbit Traps in Standard.ucl and click Open.
●
Change the Trap Shape parameter to pinch, and set Trap Mode to inverted sum
squared (at the end of the list).
The fractal should now look like this:
Next: Making a zoom movie
75
Making a zoom movie
Let's animate this fractal to make a simple zoom movie.
Make sure the animation bar at the bottom of the main
Ultra Fractal window is visible (click Options|Animation
Bar if it is not).
In Ultra Fractal, you create an animation by making
changes while Animate mode is on.
Animation bar
Animate mode
Click the Animate button on the animation bar to turn Animate mode on. The fractal
window will now show red marks at the corners and the text (Animating) in the title bar.
Look at the animation bar and note the time slider, going from frame 1 to 100. Every fractal starts
with 100 frames by default. The time slider sets the current frame, which is still frame 1 at this
point.
●
●
Move the time slider to frame 100, because we are going to animate a zoom from frame 1
up to frame 100.
Click and drag inside the fractal window to enter Select mode. Move and resize the selection
box to frame an interesting portion of the fractal. Add some rotation for a better zoom
effect.
The exact location does not matter much for this tutorial, but if you want to recreate the final movie,
position the selection box like this:
76
●
Right-click in the fractal window and click Zoom In to perform the zoom.
We are done recording the first part of our animation, so click the Animate button again to turn
Animate mode off. You should make it a habit to turn Animate mode off as soon as possible to avoid
making unwanted changes.
Next: Playing the movie
77
Playing the movie
Congratulations! You have just created a zoom movie. Let's have a look at it.
●
Move the time slider slowly back to frame 1.
Note that the fractal window immediately recalculates as soon as you move the slider to show how
the zoom is interpolated from frame 1 to frame 100. Dragging the time slider back and forth is a
convenient way of previewing the animation quickly or precisely.
To view a real-time preview of the animation,
click the Play button on the animation bar. The
animation will keep looping until you click
somewhere or hit a key.
The level of detail of the preview depends on the speed
of your computer — as long as you are using the
Guessing drawing method. To make the preview faster,
you can reduce the size of the fractal window on the
Image tab of the Fractal Properties tool window.
Any fractal in Ultra Fractal is potentially an animation. As
you have seen, you can turn any still fractal into an
animation by enabling Animate mode and changing the
fractal in some way.
Look at the time slider. Two blue dots have appeared,
one at frame 1, and one at frame 100. If you set the
slider to exactly frame 1 or 100, the corresponding dot
turns into a yellow marker to show that it is at the
current frame.
Most commands on the animation bar
are also available on the Animation
menu, with keyboard shortcuts.
The preview is always played with a
fixed frame rate. To change the preview
frame rate, click Options on the Options
menu to open the Options dialog, and
click the Fractal tab. The Animation
preview speed setting is in the
Advanced calculation options area.
See also Calculation details.
When you make changes to a fractal while Animate
mode is on, Ultra Fractal records animation keys at the
current frame, and at frame 1 if there are no animation
keys yet. The blue dots show at which frames the
animation keys are located. When you click on a dot, the
time slider jumps to the frame at which the key was
recorded.
Next: Experimenting with Animate mode
78
Animation keys
Experimenting with Animate mode
The Animate mode toggle controls how Ultra Fractal
responds to changes that you make to a fractal. The
basic rule is that if Animate mode is on, your changes
are only applied to the current frame. Otherwise, your
changes are applied to the entire animation.
Animate mode
Let's do some experiments with the rotation of the
fractal to get a feel for how this works in practice.
●
●
●
●
Move the time slider to frame 1 and verify that the Rotation Angle setting in the Location
tab is set to 0. Also note the yellow marker before the input box. This shows that this
parameter is animated and that there is a key at the current frame.
Move the time slider to frame 100. The Rotation Angle value will now probably change,
depending on how you rotated the selection box when zooming in earlier.
Set Animate Mode to on, and change the Rotation Angle value to 60.
Set Animate Mode to off, and move the time slider to frame 1 again.
Note that at frame 1, the Rotation Angle setting is still 0. That is because Animate mode was on
when you changed it at frame 100. When Animate mode is on, changes only apply to the current
frame. Let's try changing the rotation with Animate mode off to see how that works.
●
●
Make sure Animate mode is still off and the time slider is at frame 1. Change the Rotation
Angle setting to 90, which will rotate the fractal clockwise.
If you now move the time slider (slowly) to frame 100, you will see that the entire
animation has been rotated. That is because Animate mode was off when you changed the
rotation. At frame 100, you will find that the Rotation Angle setting is now 150 instead of
60. It has been increased by 90 as well.
79
You can use this technique with any parameter if you need to adjust the entire animation. For
example, you can move the animation, globally change the color density, and so on.
Let's now restore the animation to its previous state, this time by changing the keys at different
frames individually.
●
●
Make sure the time slider is still at frame 100 and enable Animate mode. Hold down the
Alt key and click and drag inside the fractal window to rotate the zoomed-in fractal at frame
100 back to its original state.
With Animate mode still enabled, move the time slider to frame 1. Enter 0 in the Rotation
Angle input box. Set Animate mode to off again.
Note that it does not matter what tools you use to make changes — the selection box, Alt-dragging,
or manually entering values. They all work together with the current state of the Animate mode
toggle.
Also, note that you can easily change the value that was recorded for an animation key simply by
going back to the frame where the key is located and adjusting the parameter while Animate mode is
enabled.
Next: Extending the animation
80
Extending the animation
Now that we have created a simple zoom movie and have learned about the Animate mode toggle, it
is time to make this animation more interesting.
●
Make sure that Animate mode is off. Go to the Outside tab and set the Threshold
parameter to 0.05.
The fractal looks much 'thinner' now. Let's animate the fractal from a really thin look to its previous
look, so it appears to grow, and then zoom in. First, we have to make the animation a bit longer to
insert a new part at the beginning.
Click the Time Settings button on the
animation bar to open the Time Settings dialog.
This dialog enables you to change the length
and the frame rate of the animation.
●
Time settings
Enter 200 in the Frames input box. In the Existing keys area, select the Keep at last
frame option. Click OK.
You have now doubled the length of the animation, with the existing zoom movie at the end of the
animation. In the animation bar, the keys that were previously located at frame 1 and 100 have now
moved to frame 101 and 200, respectively. We can now insert our 'growing' animation at the
beginning.
Make sure the time slider is at frame 1 and
set Animate mode to on.
●
Set the Threshold parameter to 0.01 so the
fractal almost disappears.
Animating parameters
●
Move the time slider to frame 120.
●
Set the Threshold parameter to 0.25. Set
Animate mode to off again.
Note that while Animate mode is on, red animation indicators appear before every parameter that
can be animated. There are also other possible indicators here:
●
●
●
●
A blue dot means that the parameter is animated. It has one or more animation keys, so it
changes somewhere during the animation.
A yellow marker means that the parameter is animated and has an animation key at the
current frame. The parameter changes to a specific value at the current frame.
Use the Play button or drag the time slider back and forth to preview the animation at this
point.
Next: Using the Timeline tool window
81
Using the Timeline tool window
Animating the Threshold parameter is a nice addition, but the animation now falls apart into two
separate parts. It would be better to start the zoom earlier, but how do we do this?
The most powerful way to edit your animations is the
Timeline tool window. It shows all parameters that can
be animated, together with an overview of the range of
frames over which they are animated.
Click the Timeline button on the animation bar
to open the Timeline tool window.
The Timeline tool window
Click the Reset View button in the toolbar to
make sure the complete animation fits in the
window.
On the left side, the Timeline tool window shows a tree view of all parameters in the fractal, grouped
by layer and category. On the right, the animated range of each category and parameter is shown.
In this case, the animated range for both the entire fractal and the Background layer ranges from
frame 1 to 200. The location is animated from frame 101 to frame 200, and the outside coloring
algorithm is animated from frame 1 to 120. Click on a category in the tree or on a range bar to see
the exact begin and end frames.
●
●
Expand the Location and Outside categories to see the individual parameters that form
the animated range of each category. Note how you can select an animation key to edit it
individually.
Move the mouse cursor over the left-hand end of the range bar of the Location category
until it changes into a resize cursor. Drag the left end to frame 30. (You can also enter 30
into the Begin Frame input box at the bottom while the Location category is selected.)
Close the Timeline tool window and preview the animation to see the effect of this change. Note how
the fractal already begins zooming at frame 30. This is good, but maybe it would be even better if
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the zoom would start slower. We can accomplish this by inserting additional animation keys
somewhere between frame 30 and frame 200.
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Move the time slider to frame 100 and set Animate mode to on.
Zoom out the fractal, and position it such that it is only slightly zoomed in and rotated
relative to the initial location. (Tip: Use Shift-dragging, Ctrl-dragging, and Alt-dragging to
achieve this. See also Normal mode.) Move the time slider back and forth while you are
working to judge the smoothness of the animation, but make sure you are only making
changes while the slider is at frame 100.
When you are finished, set Animate mode to off again.
If you have not saved the fractal already, click Save Parameters on the File menu and
save the fractal as Animated Phoenix in tutorials.upr.
Next: Adding gradient animation
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Adding gradient animation
Like any parameter in Ultra Fractal, you can also animate the gradient. Let's add some gradient
animation to let the fractal fade in from a dark grayscale gradient to its current bright colors. First,
we create the desired new gradient.
Click Gradient on the Fractal menu to open the
gradient editor.
The gradient editor works together with the Animate
mode toggle like all other tools in Ultra Fractal.
Animating gradients
Set Animate mode to on, and move the time slider to frame 20.
Click Adjust Colors on the Gradient menu.
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On the HSL tab, set Saturation to -100, which removes all color from the gradient. Set
Luminance to -40 to make the gradient darker. Click OK.
Drag the time slider back and forth to preview the result and observe that we have achieved just the
opposite what we wanted. Let's fix that.
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Move the time slider to frame 1. Make sure the gradient editor is active and Animate mode
is still on.
Click Copy on the Edit menu to copy the gradient to the Clipboard, as it is at the current
frame. It is important that Animate mode is on while you copy the gradient, otherwise you
would have copied all animation keys as well. We just want the gradient as it is at frame 1.
Move the time slider to frame 140, and click Paste on the Edit menu. Again, Animate
mode must be on, because we want the paste operation to affect the current frame only.
Otherwise, the gradient for the entire animation would have been replaced by the pasted
gradient.
Turn off Animate mode and drag the time slider back and forth again to view the effect. This is
almost what we want, except that the dark gradient should be at the start of the animation. We can
fix that with the Timeline tool window.
Click Timeline on the animation bar to open the Timeline tool window. Scroll down and
expand the Gradient category, its Color category, and all its four control points.
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Click on the leftmost animation key of the Color parameter of Control Point 1 to select it.
Hold down the Ctrl key and click on the leftmost keys of Control Point 2 to 4 as well to
add them to the selection. The timeline should look like the left picture below.
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Click the Delete Selection button to delete these four animation keys. The timeline should
now look like the right picture above.
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Finally, click on the range bar for the Gradient category to select it, and then drag its left
edge to frame 1. The Gradient bar should now range from frame 1 to frame 140.
Drag the time slider back and forth to view the effect in the fractal window. This is what we wanted,
but it turns out that frame 140 is too late — almost the entire animation is now quite dark and gray.
Let's fix this as well.
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In the Timeline tool window, drag the right edge of the range bar for the Gradient
category to frame 60.
Again, examine the effect with the time slider and experiment until you are satisfied.
Next: Adding a new layer
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Adding a new layer
As a final step, we are going to extend the animation once again, this time at the end, to add a final
fade to a new layer. First, we will create a new layer.
Click the Add button on the Layers tab of the
Fractal Properties tool window to duplicate the
Background layer.
The new layer is a complete duplicate of the background
layer, with all its animation keys. Because the new layer
is going to be hidden most of the time, a static layer is
good enough and it saves valuable calculation time.
Therefore, it would be better to remove the animation
keys.
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Animating layers
Make sure the time slider is at frame 200 and open the Timeline tool window.
Click on the range bar for the Layer 1 category, and click the Delete Selection button to
delete all animation keys for Layer 1. You can close the Timeline tool window now.
Layer 1 is no longer animated now. Because the time slider was at frame 200, all previously
animated parameters have been set to the value they had at that frame.
Click the Browse button on the Outside tab of the Layer Properties tool window to choose a
new coloring algorithm. Select Triangle Inequality Average in Standard.ucl and click
Open.
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On the Layers tab of the Fractal Properties tool window, select Hard Light as the merge
mode for Layer 1.
Now, the idea is to extend the animation to 250 frames, and let this new layer fade in, beginning at
frame 200.
Click the Time Settings button on the animation bar to open the Time Settings dialog. Set
Frames to 250, and select Keep at first frame. Click OK.
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First, set the opacity slider for Layer 1 to 0%, as this is the initial value.
If we would enable Animate mode and change the opacity at frame 250, the opacity would be
animated from frame 1 to frame 250. We could then rescale that to the range 200-250 using the
Timeline tool window, but there is an easier way.
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Ensure the time slider is at frame 200. Rightclick on the opacity slider and click Insert
Key on the menu that pops up. This inserts a
new key for the opacity parameter at frame
200, with the current value (0%).
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Editing animations
Move the time slider to frame 250 and set Animate mode to on. Change the opacity
slider to 100%. Set Animate mode to off again.
Examine the results by dragging the time slider. Note that the opacity animates from 0% at frame
200 to 100% at frame 250, just as we intended.
Next: Rendering the animation
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Rendering the animation
Now that the animation is finished, you can preview it with the Play button. However, you will
probably want to view it as an AVI file with much higher quality. For that, you have to render the
animation first.
Click Render to Disk on the Fractal menu to
open the Render to Disk dialog.
The Render to Disk dialog looks a bit different than you
might be used to, because it contains options specific to
animations that are normally hidden.
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Rendering animations
From the File Format drop-down list, choose AVI movie. The Export Options dialog will pop
up so you can set additional options for the AVI format.
The list of compressors depends on what is installed on your computer. Some are better
suited to fractal movies than others — it is best to experiment. For now, choose Cinepak
Codec by Radius, set Quality to 100% and Key frame to once in every 15 frames. Click
OK.
If you prefer a different destination file than what Ultra Fractal automatically suggests, enter
it into the Destination File input box, or click its Browse button.
In the Animation area, set Frame Range to Entire Animation. You can use this option to
render only a selected range of frames, or just the current frame.
Set Motion Blur to Normal. This applies a motion blur effect to animated zooms, which
makes them smoother and more natural-looking.
The other options are the same as when rendering still images. You can set them as you prefer, but
make sure to enable anti-aliasing for the best results. If you check the Open when finished option,
Ultra Fractal will automatically open the resulting AVI file in the default player, for example Windows
Media Player.
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Click OK to start rendering. The Render to Disk tool window opens to display the rendering
progress. Since animations are much more complex to calculate than still fractals, the
render can easily take an hour or more, depending on the width and height that you
selected for the final movie.
Congratulations! You have made it to the end of this tutorial. We have used most of the animation
features of Ultra Fractal to make this animation, and you probably have many ideas for your own
animations now.
For more information, please refer to the Animation chapter of the help file. Enjoy!
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What are fractals?
Ultra Fractal creates images of fractals. Fractal images are created by
repeatedly calculating a fractal formula. Although these formulas are
purely mathematical, the resulting pictures are often very beautiful and
complex.
Ultra Fractal goes a long way toward hiding the mathematical stuff.
Instead, you focus on the fractals themselves, the way they are
combined, and how they are colored. This enables you to turn your
fractals into true works of art.
This chapter will explain the basics of fractals, and why they are so interesting.
Next: Self-similarity
See Also
Tutorials
Workspace
Fractal windows
89
Self-similarity
There are various definitions of what a fractal is. One of the easiest is that a fractal is usually selfsimilar. That means that it repeats itself. For an example, look at the following fractal.
This is a Van Koch fractal. It is based on a very simple shape.
To create the fractal, the flat lines are replaced by the entire shape itself.
This process is repeated again and again to create an infinitely complicated fractal. Still, every part
of the fractal contains the original shape. We say that the fractal is self-similar. Most fractals in Ultra
Fractal are calculated differently, but the principle of self-similarity still applies.
This is also the reason that it is so popular to zoom into fractals: there are always more details to be
discovered, no matter how far you zoom.
Next: Julia sets
See Also
What are fractals?
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Julia sets
One of the most basic fractal types is the family of Julia sets, discovered by the French mathematician
Gaston Julia during the first World War. Julia sets are created by a simple formula with one complex
parameter called c or seed. This parameter can be varied to create many variations. Here are a few
examples.
Julia sets are also self-similar, as illustrated by the following zooms into the last image above. The first
zoomed image shows the top of the original. Further zooms are illustrated by the small red rectangles in
the images.
The same spiral-like shape is repeated over and over again.
It can be difficult to find good values of the c parameter. Fortunately, the Mandelbrot set, which is
discussed next, can help you with that.
Next: The Mandelbrot set
See Also
What are fractals?
Julia
91
The Mandelbrot set
The Mandelbrot set, discovered in 1980 by Benoit Mandelbrot, is probably the most famous fractal. Like
Julia sets, it is generated by a very simple formula, but it is incredibly complex.
The Mandelbrot set is loosely self-similar: parts of the original fractal appear again when zooming in, but
often deformed and with different ornaments. This is what makes it so rewarding to zoom into this
fractal: you never know what you will see next.
This is illustrated by the following short zoom, starting at the very left of the Mandelbrot set shown
above. As you zoom in, you see copies of the original Mandelbrot set, but with different surroundings.
Another interesting aspect of the Mandelbrot set is that it is actually a map of all Julia sets. Each point
corresponds to a Julia set. Points inside the Mandelbrot set (here shown as black) are connected Julia
sets; points outside the Mandelbrot set tend to give more disorganized Julia sets.
With the switch feature in Ultra Fractal, you can easily pick a point of a Mandelbrot fractal to see the
corresponding Julia set. This is the best way to discover interesting Julia sets.
Next: Fractals today
See Also
What are fractals?
Mandelbrot
Julia sets
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Fractals today
While Ultra Fractal is well suited to exploring the classic fractal types
discussed so far, it can do much more than that. There are many more
fractal types to choose from, and you can even write your own fractal
formulas (or use formulas written by other people). Most fractal types
are variations on the Mandelbrot and Julia sets.
Each fractal type can be combined with various coloring algorithms,
each capable of coloring the fractal in a different way. Transformations can be added to distort the
shape of the fractal. Colors are easy to change and tweak with the gradient editor. On top of that,
you can use multiple layers to combine different fractals or different coloring methods to form the
final image.
Because of these changes, fractals have grown from a mathematical curiosity to a respected form of
art. There are fractal exhibitions in museums and galleries all over the world. There is a large
number of online galleries on the web, where you can purchase prints and posters from various
fractal artists.
Next: Where to start
See Also
What are fractals?
Fractal windows
93
Where to start
Now that you know a bit more about fractals, you are probably wondering how to produce these with
Ultra Fractal. By default, Ultra Fractal opens with a standard Mandelbrot fractal, so the easiest way is
to take this fractal and start zooming.
Click and drag inside the fractal window to open the selection box. Drag and resize it, and then
double-click inside the selection box to zoom in.
Ultra Fractal has many more possibilities, but it is a good idea to start with simple zooming to get a
feeling for what fractals are and how Ultra Fractal works. Also, be sure to work through the tutorials
to learn more.
See also
Tutorials
Workspace
94
Workspace overview
Ultra Fractal has one main application window that contains all open documents, such as fractals,
gradients, and formula files. Secondary windows, called tool windows, edit the properties of
fractals and provide access to other functionality.
The workspace contains the following elements:
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Document windows contain the documents that you work on, such as fractals and
gradients. In the screen shot above, the fractal window is an example of a document
window.
The buttons on the toolbar provide access to frequently-used commands. Usually, these
commands can also be accessed through the pull-down menu directly above the toolbar.
The toolbar can be hidden and restored by clicking Toolbar on the Options menu.
The dock bar is a place to store tool windows, to keep them from using too much screen
space. Tool windows can be dragged into and out of the dock bar at any time. Tool windows
in the dock bar are called docked tool windows. They can also be collapsed so you only
see the title bar. To hide and restore all tool windows and the dock bar, click Tool Windows
on the Options menu or press F12.
Floating tool windows are tool windows that float freely over the screen, instead of being
in the dock bar. This is useful if you use a tool window a lot, or to place some tool windows
on a secondary monitor if you have one. The Timeline tool window works better when
floating than when docked.
The animation bar contains animation controls for the active fractal window. See Animation
bar. (Ultra Fractal Animation Edition only)
95
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The status bar provides additional information about the active document window, such as
the elapsed calculation time for a fractal. To hide and restore the status bar, click Status Bar
on the Options menu.
The window panel is an area in the status bar that lists all open document windows, much
like the Windows task bar. To bring a document window to the foreground, click on its button
in the window panel. To hide and restore the window panel, click Window Panel on the
Options menu.
Next: Working with tool windows
See Also
Tutorials
Fractal windows
Gradients
96
Working with tool windows
Most of the functionality in Ultra Fractal is accessed through the various tool windows. All tool
windows are resizeable. They can be put in the dock bar to save screen space, or they can float on
the screen for easy access.
With docked tool windows:
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Use the title bar to drag a tool window out of the dock bar to change it into a floating tool
window.
Drag the resize bar up and down to change the height of a tool window.
Click the hide tool window button to temporarily hide a tool window, to make more space
for the other windows. The tool window collapses to show only the title bar.
Click the restore tool window button to restore a hidden tool window.
Click the help button and then click a control inside the tool window to get context-sensitive
help.
Click the show/hide dock bar button to hide the entire dock bar temporarily. Drag the
vertical bar to the left and right to change the width of the dock bar.
With floating tool windows:
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Use the title bar to drag the tool window around. Drop it on the dock bar to change it into a
docked tool window.
Click the help button and then click a control inside the tool window to get context-sensitive
help.
Click the close button to hide the tool window. To show it again, click Tool Windows on the
Window menu, and then click the name of the tool window.
Right-click on the title bar and click Decrease Opacity to make the tool window transparent,
so you can see the windows beneath it.
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In general:
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Click Tool Windows on the Window menu for a menu listing all tool windows. Click the name
of a tool window to show and hide it. Right-clicking the dock bar will also show this menu.
Click Tool Windows on the Options menu or press F12 to hide and restore all tool windows.
Next: Tool windows overview
See Also
Workspace overview
General keyboard shortcuts
98
Tool windows overview
There are two categories of tool windows in Ultra Fractal. Most tool windows work with the active
fractal document, but there are also stand-alone tool windows that work indepently.
Tool windows that work with the active fractal document:
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The Layer Properties tool window edits the active layer of the fractal. This is where you do
most of the work, for example changing fractal types or experimenting with parameters.
The Fractal Properties tool window edits the properties that apply to the entire fractal, such
as the image size and the layers that it contains.
The Fractal Mode tool window controls what happens and provides feedback when you click
and drag inside the fractal window.
The Timeline tool window shows all parameters in the active fractal window, grouped by
category, and enables you to edit their animation properties. (Ultra Fractal Animation Edition
only.)
The Statistics tool window shows additional information about the fractal and the calculation
process.
The Color Cycling tool window animates the colors in the fractal.
Stand-alone tool windows:
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The Network tool window manages the computers that are connected to Ultra Fractal for
distributed fractal calculations. (Ultra Fractal Animation Edition only.)
The Render to Disk tool window manages background calculations of disk render jobs.
The Compiler Messages tool window collects warnings and errors generated by the formula
compiler when you select or reload a formula.
Next: Options dialog
See Also
Working with tool windows
Workspace overview
99
Layer Properties tool window
The Layer Properties tool window edits the selected layers in the active fractal window. Layers are
selected in the Layers tab of the Fractal Properties tool window. The title bar shows which layers are
currently being edited.
To open the Layer Properties tool window if it is hidden, click Tool Windows on the Window menu,
and then click Layer Properties.
The Layer Properties tool window contains five tabs:
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The Location tab specifies the coordinates of the layer. The coordinates define which portion
of the fractal is visible. The coordinates are shown in two different forms: as the center
coordinate with magnification, and as the coordinates of the corners of the layer. Although it
is possible to enter coordinates directly here, you will usually use the zooming, panning and
rotating capabilities of the fractal window instead. The Copy and Paste buttons are useful for
copying locations from one layer or fractal to another. The Reset button resets the location
to the default for the currently selected fractal formula.
The Mapping tab contains a list of geometric transformations that are applied to the layer.
These are used to transform the shape of a fractal.
The Formula tab specifies the fractal formula (fractal type) that is used by the layer. The
fractal formula defines the shape of the fractal.
The Inside and Outside tabs specify how the data from the fractal calculations is
interpreted to obtain the final coloring of the layer. By selecting different coloring algorithms
here and adjusting the parameters, many different images can be created with the same
fractal formula. See also Inside and outside.
To understand how the controls on the tabs work together, it helps to remember that in a way, the
calculation "flows" through the tabs from left to right, starting with the location, and ending with the
coloring algorithms.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
Keyboard shortcuts for the Layer Properties tool window
Tool windows
100
Fractal Properties tool window
The Fractal Properties tool window edits global properties of the active fractal window, such as the
size of the image, the list of layers, history, and comments.
To open the Fractal Properties tool window if it is hidden, click Tool Windows on the Window menu,
and then click Fractal Properties.
The Fractal Properties tool window contains four tabs:
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The Layers tab manages the layers in the fractal. Here, you can control how the layers are
merged together to produce the final image. The properties of individual layers are edited by
the Layer Properties tool window.
The Image tab specifies the dimensions of the fractal window. It is important to remember
that the fractal window is really only a preview. Use the Render to Disk feature to create final
images at any size, independent of the size of the fractal window. See also Resolution.
The History tab shows the previous states of the fractal. It allows you to go back any
number of steps in time, without recalculations. See Fractal history list.
The Comments tab provides a space for you to type comments on the fractal, such as
copyright information. It also contains the credits list that automatically tracks the artists
that have worked on the fractal, so everyone receives proper credit.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
What are fractals?
Keyboard shortcuts for the Fractal Properties tool window
Tool windows
101
Fractal Mode tool window
The Fractal Mode tool window controls how mouse operations are interpreted by the active fractal
window, shows context-sensitive help, and it provides live previews for the Explore and Eyedropper
features.
To open the Fractal Mode tool window if it is hidden, click Tool Windows on the Window menu, and
then click Fractal Mode. The Fractal Mode tool window will open automatically when it is needed to
show previews.
Use the buttons on the left to select the active mouse mode for fractal windows:
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In Normal mode, click and drag while holding down the Shift, Ctrl, or Alt keys to zoom,
pan, rotate, skew, and stretch the fractal. Clicking and dragging without holding down a shift
key enters Select mode by default. Double-click to zoom in twice. All mouse bindings are
customizable in the Mouse tab of the Options dialog. The Fractal Mode tool window shows the
current bindings.
In Select mode, a selection box is used to zoom. The area inside the box is expanded to fill
the entire fractal window when you zoom in. The Fractal Mode tool window shows a preview
of the new fractal, and contains additional options.
Switch mode is used to switch from Mandelbrot-like fractals to their Julia counterparts. This
is possible because the Mandelbrot set is actually a map of Julia sets. Move the mouse cursor
over the fractal and the Fractal Mode tool window will show a preview of the Julia set that
corresponds to the point under the cursor. Click to open a new fractal with this Julia set.
If the Fractal Mode tool window is open and Normal mode is selected, it also shows context-sensitive
help for the control that is currently under the mouse cursor. This also works for formula parameters.
See Getting help.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control.
See Also
Normal mode
Select mode
Switch mode
Tool windows
102
Statistics tool window
The Statistics tool window shows additional information on the active fractal window. To open the
Statistics tool window if it is hidden, click Tool Windows on the Window menu, and then click
Statistics.
The General tab shows the calculation progress of the fractal at the top. At the bottom, several
statistics on the active layer are shown, such as the precision of the calculations used, the
percentage of pixels that were actually calculated (not guessed), and the iteration limits of the pixels
calculated so far.
The Iterations tab shows a histogram with detailed information on how the iterations values are
distributed. You can use this information to estimate a good value for the Maximum Iterations setting
in the Formula tab of the Layer Properties tool.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
Arbitrary precision
Maximum iterations
Tool windows
103
Color Cycling tool window
The Color Cycling tool window rotates the colors of the layers in the active fractal. To open the Color
Cycling tool window if it is hidden, click Tool Windows on the Window menu, and then click Color
Cycling.
Click on one of the buttons to start cycling the colors. Move the slider to change the cycling speed.
What color cycling does is repeatedly moving the Rotation slider of the gradients of the editable
layers in the fractal. This rotates the gradients in the layers, reproducing the "palette animation"
effect that is well-known from older 256-color fractal programs.
Color cycling is also possible without the Color Cycling tool window. Right-click inside the fractal
window to open a pop-up menu, click the Gradient submenu and then click Cycle Colors Forward or
Cycle Colors Backward. These commands are available in Full-screen mode as well.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
Gradients
Tool windows
104
Network tool window
Note: You need Ultra Fractal Animation Edition for network calculations.
The Network tool window manages connections to other computers on the network. Ultra Fractal can
then use these computers to distribute fractal calculations, so they are performed much faster.
To open the Network tool window if it is hidden, click Tool Windows on the Window menu, and then
click Network.
With the list of connections in the tool window, you can add, rename, edit, and delete connections.
Connections can also be enabled and disabled. By clicking on a connection, you can see its status,
how long it has been connected, and how many pixels per second are calculated by the connected
computer on average.
It is important to understand that the network tool window shows and edits the connections, but it
does not "own" them. So, even when you hide or close the tool window, the connected computers
will still continue to be used.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
Network calculations
Connections
Tool windows
105
Render to Disk tool window
The Render to Disk tool window manages render jobs. Fractals and animations can be rendered to
disk to create high-resolution images and fractal movies with better quality than is possible in the
fractal window. Each render command creates a render job that is subsequently performed in the
background. The Render to Disk tool window shows the list of render jobs that are still to be finished.
To open the Render to Disk tool window if it is hidden, click Tool Windows on the Window menu, and
then click Render to Disk.
Render jobs are calculated from the top of the list to the bottom, with new jobs added at the bottom.
You can add, delete, pause, and resume render jobs. Multiple jobs can be calculated simultaneously.
It is important to understand that the Render to Disk tool window shows and edits the render jobs,
but it does not "own" them. So, even when you hide or close the tool window, the jobs will still
continue to be calculated normally.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
Exporting and rendering
Render jobs
Tool windows
106
Compiler Messages tool window
The Compiler Messages tool window collects warning and errors generated by the compiler when you
select or reload a formula. These messages are intended for formula authors. If you encounter errors
in a formula that you did not write yourself, it is best to contact the author of the formula.
To open the Compiler Messages tool window if it is hidden, click Tool Windows on the Window menu,
and then click Compiler Messages.
The tool window attaches itself to the most recently compiled formula. It also shows any run-time
messages generated by the attached formula when it is used for fractal calculations. Run-time
messages can be used for debugging purposes.
Double-click a message to open the line of code that corresponds to the message in the formula
editor, so you can inspect the code and correct the error. Click the Help on Error button to get help
about the selected message.
For more information on a specific control, click the help button in the title bar of the tool window,
and then click the control, or move the mouse over the control while the Fractal Mode tool window is
open.
See Also
Writing formulas
Debugging
Tool windows
107
Options dialog
The Options dialog provides a single place to customize Ultra Fractal according to your personal
preferences.
Click Options on the Options menu to open the Options dialog.
The options are grouped by several tabs:
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The Mouse tab enables you to customize the mouse actions for the fractal window to zoom,
pan, rotate, and so on. It also contains options for double-clicking and zooming, and for the
Switch feature.
The Fractal tab contains options for fractal windows. See also Calculation details and Playing
animations.
The Defaults tab specifies the default settings for fractal windows. See also Default fractal.
The Gradient tab sets an optional default gradient.
The Editor tab contains options for formula editors.
The Syntax tab enables you to customize the syntax highlighting colors for various language
elements in the formula editor.
The Browser tab contains options for browsers, such as template parameter sets for
previews and thumbnail cache settings.
The Environment tab contains general workspace options.
The Folders tab enables you to change the location of the various document folders used by
Ultra Fractal.
To get help on individual settings, click the
click the setting that you want help for.
button in the title bar of the Options dialog, and then
The Options menu also provides commands to show and hide various user interface elements, and to
update your collection of public formulas.
See Also
Workspace overview
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Fractal windows
Fractal windows contain the fractals that you work on in Ultra Fractal. While you edit the fractal using
the Fractal Properties and Layer Properties tool windows, the fractal window is continually updated to
show the result of your changes.
Note: Although fractal windows are resizeable, this does not change the size of the fractal itself.
Use the Image tab in the Fractal Properties tool window to resize the fractal.
The toolbar contains commands to edit and save the fractal:
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The New button creates a new fractal from scratch. To duplicate the current fractal instead,
click Duplicate on the File menu.
The Open and Browse buttons open files from disk.
The Save button saves the fractal to disk. See Opening and saving fractals.
The Undo and Redo buttons can undo and redo your previous actions. See Fractal history
list.
The Copy and Paste buttons copy fractal parameters to and from the Clipboard. See
Copying and pasting fractals.
The Gradient button opens the gradient editor associated with the fractal window to edit the
colors of the fractal.
The mouse mode buttons show and select the active mouse mode. The mouse mode
determines what happens when you click and drag inside the fractal window. There are three
mouse modes:
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Normal mode
❍
Select mode
❍
Switch mode
The Save Parameters button saves the fractal to a parameter set. See Parameter files.
The Render to Disk button starts rendering the fractal or animation to disk, creating a highresolution image or a fractal movie with better quality than possible in the fractal window.
See Rendering images.
The commands on the toolbar are duplicated on the File, Edit, and Fractal pull-down menus.
Frequently used commands are also on the menu that pops up when you right-click inside the fractal
window.
Next: Normal mode
See Also
Keyboard shortcuts for fractal windows
Animation
Exporting and rendering
Workspace
109
Normal mode
The mouse mode determines what happens when you click and drag inside the fractal window. By
default, a fractal window is in Normal mode.
To put the fractal window in Normal mode, click Normal Mode on the Fractal menu, or make sure
the Normal mode button in the toolbar is down.
In Normal mode, you can zoom, pan, rotate, stretch, and skew the fractal simply by clicking and
dragging inside the fractal window. Before you click, hold down one of the Ctrl, Shift, or Alt keys to
indicate what you want to do.
To:
Do this:
Zoom
Hold down Shift, click and drag
Pan
Hold down Ctrl, click and drag
Rotate
Hold down Alt, click and drag
Stretch
Hold down Shift and Ctrl, click and drag
Skew
Hold down Ctrl and Alt, click and drag
Enter Select mode
Click and drag
While still holding down the left mouse button, move the mouse around to make adjustments. The
fractal window continually shows a preview of the result. In the status bar, additional information is
shown, such as the current rotation angle.
The status bar also shows extra keys that you can hold down for fine adjustments or to constrain
rotation to 45° increments, for example. To use them, first release the key that you have been
holding down (still holding down the left mouse button) and then press and hold down the
appropriate key.
When you are finished, release the mouse button and the fractal will recalculate to apply your
changes. To cancel the operation while you are still holding down the left mouse button, briefly click
the right mouse button. If you have already released the mouse button, click Undo on the Edit menu
to undo the operation.
Notes
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The table above displays the default set of actions. Use the Mouse tab in the Options dialog
to customize them. The Fractal Mode tool window always shows the current key bindings.
If the fractal contains multiple layers, only the editable layers are affected.
To move the fractal very precisely with the keyboard, hold down Ctrl and use the arrow keys
to pan in steps of one pixel. Hold down Shift as well to increase the step to ten pixels. See
also Keyboard shortcuts.
Next: Select mode
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See Also
Animating locations
Fractal windows
111
Select mode
The mouse mode determines what happens when you click and drag inside the fractal window. In
Select mode, a selection box is used for zooming, panning, rotating, stretching, and skewing.
To enter Select mode from Normal mode, simply click and drag inside the fractal window.
Alternatively, click Select Mode on the Fractal menu, or make sure the Select mode button in the
toolbar is down.
In the fractal window, a selection box appears.
The area inside the selection box will be magnified to fill the fractal window when you zoom in. You
can manipulate the selection box by dragging the handles and edges.
To:
Do this:
Move the selection box
Click inside the box and drag
Resize the selection box
Drag the edges or the handles at the corners
Rotate the selection box
Drag the top handle
Stretch the selection box
Hold down Ctrl and drag the edges or the handles at the corners
Skew the selection box
Hold down Ctrl and drag the top handle
Cancel
Click outside the selection box
When you are finished, double-click inside the selection box to zoom in. To zoom out, hold down Ctrl
while double-clicking. Alternatively, right-click inside the fractal window to open a menu with the
following commands:
Zoom In
Magnifies the area inside the selection box to fill the fractal window
Zoom Out
Shrinks the area of the fractal window to fill the selection box
Crop
Resizes the fractal window to fill the selection box
Reset
Restores the default position of the selection box
Resize Fractal
Resizes the fractal window to match the aspect ratio of the selection box
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Stretch Fractal
Stretches the fractal window to fit the selection box
While you are working with the selection box, the Fractal Mode tool window shows a preview of the
resulting fractal. The buttons in the tool window select what you want to do: zoom in, zoom out, or
crop. They duplicate the menu commands listed above, except that they are not applied until you
click the Apply button in the tool window.
Notes
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While the selection box is visible, the status bar provides additional information, such as the
current magnification and rotation angle.
If the fractal contains multiple layers, only the editable layers are affected.
Next: Switch mode
See Also
Tutorial: Learning basic skills
Keyboard shortcuts in Select mode
Animating locations
Fractal windows
113
Switch mode
The mouse mode determines what happens when you click inside the fractal window. In Switch
mode, a mouse click switches between related fractal types.
To enter Switch mode, click Switch Mode on the Fractal menu, or make sure the Switch Mode
button on the toolbar is down.
Switching is typically used with Mandelbrot and Julia-like fractals. The Mandelbrot set is actually a
map of Julia sets. Each point in the Mandelbrot set corresponds to a unique Julia set. The shape of
this Julia set reminds of the immediate surroundings of the corresponding point in the Mandelbrot
set.
If you enter Switch mode while looking at a Mandelbrot set and move the mouse cursor over the
fractal window, the Fractal Mode tool window shows a preview of the corresponding Julia set. Click to
open a new fractal window with this Julia set, so you can further explore it.
Notes
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The Explore and Eyedropper features are similar to the switch feature, but they work with all
parameters and are much more flexible.
Sometimes the preview remains static while you are moving the mouse cursor. In this case,
the fractal is not a map of the fractal to switch to, for example when you are working with a
Julia set. Just click anywhere to switch to the corresponding Mandelbrot set.
If the fractal has multiple layers, Ultra Fractal uses the active layer for switching.
The Mouse tab in the Options dialog contains several options for Switch mode, such as the
option to open the Julia set in the same fractal window, to copy the coloring of the original
fractal, and so on.
The fractal formula contains switch settings that control how Switch mode works. Refer to
the compiler documentation if you want to add switching support to your own formulas.
Next: Opening and saving fractals
See Also
Tutorial: Learning basic skills
Explore
Eyedropper
Fractal windows
114
Opening and saving fractals
Fractals are saved to fractal files (*.ufr). A fractal file contains one fractal, complete with the
calculated pixels and all the information required to restore it. Because the calculated pixels are
saved as well, fractal files can become quite large. However, the fractal does not have to be
recalculated when opening the file.
To save a fractal to a fractal file, click Save on the File menu. If the fractal has not been
saved before, a file dialog will pop up, where you can type a name for the fractal.
To open a previously saved fractal file, click Open on the File menu. In the file dialog, set
the File type input box to Fractal files and select the fractal you want to open. The fractal will
be opened in a new fractal window.
At the bottom of the File menu, there is a list of recently opened files. Simply click the name of a file
to open it.
Fractal files are a good choice if you want to save fractals for your own reference, for example to a
hard disk or CD. However, if you want to share your fractals with other Ultra Fractal users, it is
better to use parameter files or copying and pasting.
Notes
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Fractal files are saved in a proprietary format. If you want to import your fractals in graphics
software such as Adobe Photoshop, you need to export or render the fractal first.
You can change the number of recently opened files displayed at the bottom of the File menu
in the Environment tab of the Options dialog.
Next: Parameter files
See Also
Tutorial: Learning basic skills
Browsers
Fractal windows
115
Parameter files
Fractals can be saved as parameter sets as well as in fractal files. Parameter sets are much smaller
than fractal files because they do not contain the calculated pixels. That means that the fractal has to
be recalculated when a parameter set is opened. Parameter sets are ideal for sharing fractals with
other users on the Internet.
Parameter sets are stored in parameter files. A parameter file (*.upr) can contain any number of
parameter sets. This makes it easy to store and organize collections of parameter sets. Parameter
files are stored as plain text and can be opened in text editors such as Notepad or the built-in
formula editor.
To save a parameter set, click Save Parameters on the File menu. The Save Parameters
browser will open. You can save the parameter set in an existing parameter file or in a new
file. Type the name of the file and the title of the parameter set and click Save.
To open a previously saved parameter set, click Browse on the File menu. This opens a
modeless browser. Select the parameter file that contains the parameter set that you want
to open, and then double-click the parameter set inside the file.
You use browsers to organize and manage your parameter sets and parameter files, as well as other
files that contain multiple entries, such as formula files. See Browsers.
Notes
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By checking the Save Formulas checkbox when saving a parameter set, the formulas used
by the fractal are embedded in the parameter file. When opening the parameter set, they will
be installed if they are not already present in the formulas folder. Check this option when
you are going to send the parameter file to another user (but not on the mailing list).
Parameter sets larger than 2 KB are saved in a compressed format. To save them without
compression, open the Options dialog and uncheck the Compress parameter sets larger than
2 KB option in the Fractal tab. This is necessary if you want to edit the parameter files
manually.
Ultra Fractal can also import most Fractint parameter sets in PAR files (*.par). They can be
opened just like other parameter files.
Next: Copying and pasting fractals
See Also
Quick Start Tutorial
Fractal windows
116
Copying and pasting fractals
Fractals can easily be shared between fractal windows and even between Ultra Fractal users by
copying them to the Windows Clipboard.
To copy a fractal to the Clipboard, click Copy on the Edit menu. The Clipboard now contains
a parameter set describing the fractal in plain text format. You can paste it into another
fractal window, but you can also share it with other Ultra Fractal users just by pasting it into
an email message (for example in Outlook).
To paste a fractal on the Clipboard into an open fractal window, click Paste on the Edit
menu.
To open a fractal that you have received via email, select the entire parameter set in the email
message:
and then copy it to the Clipboard (in most email software, such as Outlook, press Ctrl+C). Now open
a new fractal window in Ultra Fractal (click New > Fractal on the File menu), and click Paste on the
Edit menu to paste the parameter set into the fractal window.
Notes
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Click Copy Formulas on the Edit menu to copy a fractal to the Clipboard, including the
formulas that it uses. This enables other users to open it regardless of the formulas that they
have installed on their computer. (Do not use this option on the mailing list, though.)
Click Copy Image on the Edit menu to copy the image of the fractal to the Clipboard so you
can paste it into a document or a graphics editor like Paint. However, you can create larger,
higher-quality images by rendering them.
Next: Fractal history list
See Also
Ultra Fractal mailing list
Parameter files
Fractal windows
Editing animations
117
Fractal history list
Every fractal has a history list. The history list stores previous states of the fractal, so you can easily
undo and redo your changes. Because the calculated pixels are saved as well, the fractal does not
have to be recalculated when undoing changes. This gives you the freedom to explore in the
knowledge that you can always effortlessly go back to a previous state, without having to wait.
To go back to the previous state of the fractal, click Undo on the Edit menu.
To cancel the last Undo operation, click Redo on the Edit menu.
The History tab in the Fractal Properties tool shows a list of previous states of the fractal, complete
with previews and descriptions. To go back to a previous state, simply click it.
Next: Full screen mode
See Also
Fractal windows
118
Full screen mode
A fractal window can be maximized to full screen mode so you can see and explore the fractal
without being distracted by other windows.
To enter full screen mode, click Full Screen on the Fractal menu. The fractal will now appear full
screen. To go back to the normal fractal window, right-click to open a pop-up menu and click Full
Screen again.
In full screen mode, a limited number of operations are available through the pop-up menu. You can
fully use Normal mode, Select mode and Switch mode to explore the fractal, although without the
help of the Fractal Mode tool window. The menu also offers undo and redo commands.
The Gradient submenu provides some additional commands to alter the colors of the fractal.
Although this submenu is also available in the normal fractal window, it is especially useful in full
screen mode, where you cannot access the gradient editor.
Most fractal window keyboard shortcuts, such as the commands on the Animation menu, also
function in full screen mode.
Randomize
Randomizes the colors of the gradient. There are four different options.
Adjust Colors
Opens a dialog to adjust the colors of the gradient. See Adjusting gradients.
Cycle Colors
Cycles the colors of the gradient forward or backward. See Color Cycling.
Next: Default fractal
See Also
Keyboard shortcuts for fractal windows
Fractal windows
119
Default fractal
When you start Ultra Fractal, a new fractal window is opened automatically with the default fractal.
You can use this fractal as a base to create your own fractals.
However, you may wish to modify some of the default settings. For example, you might want to have
a different gradient, a different fractal formula, a larger number of frames, and so on.
To change the default fractal, simply modify it as you wish. Then, save it as a parameter set with a
new name. For example, you can save it as 'My Default Fractal' in the file 'My Fractals.upr'.
Click Options on the Options menu to open the Options dialog. On the Defaults tab, select
the parameter set you just saved as the Default parameter set.
From now on, this parameter set will be opened when you start Ultra Fractal.
Notes
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On the Defaults tab of the Options dialog, you can also set the default size of the fractal
window, and specify that this should override any parameter sets that you open. It is also
possible to set up default copyright and comments notices.
On the Environment tab, you can also select a different action on startup than loading the
default parameter set.
It is not recommended to save anything to the Examples.upr file that is installed with Ultra
Fractal. Use the My Fractals.upr file or other files instead.
Next: Copyright and tweaking
See Also
Parameter files
Fractal windows
120
Copyright and tweaking
If you want to create your own fractals to perhaps display them on a web site or to sell prints, it is
important to respect copyright issues and make sure you own your fractals completely. Fortunately,
this is quite straightforward.
The best way to be sure that you are creating an original new fractal is by starting from scratch. You
can either start from the default fractal that is opened when starting Ultra Fractal, or by clicking New
on the File menu, and then Fractal. You can freely use all formulas, transformations, and coloring
algorithms that come with Ultra Fractal or that are in the public formula database.
If you start a fractal by modifying someone else's fractal, creating something original is less easy.
The general consensus is that if you make enough modifications so that your fractal does not look
like the original fractal anymore, the copyright from the original fractal no longer applies. This could
include selecting different fractal formulas or coloring algorithm, zooming in or out, modifying
parameters, and so on. The distinction between making enough modifications and barely changing
the original fractal is subjective, of course. Therefore, you should always contact the creator of the
original fractal to ask for permission before considering your derived fractal to be yours only.
As mentioned above, formulas are free to use. However, modifying formulas is another issue.
Generally, you can modify formulas for your own use, but you may not distribute them. If you want
to distribute a modified formula, you must ask the original formula author for permission first.
Next: Calculation details
See Also
Fractal windows
Public formulas
Mailing list
Writing formulas
121
Calculation details
Tip: This slightly technical topic explains how multi-threading in Ultra Fractal works and how its
settings can be adjusted. However, you don't need to know this in order to work with Ultra Fractal.
Ultra Fractal is fully multi-threaded [1] and can take advantage of multi-processor computers to
speed up fractal calculations. This is done by splitting the fractal into multiple parts so the processors
can work on each part in parallel. You can even distribute calculations to other computers with the
network calculations feature.
This works well with most Mandelbrot-type fractals, where each pixel of the fractal can be calculated
independently. However, with fractal types such as IFS and Flame Fractals [2], the entire image is
calculated in one step and it cannot be subdivided. Therefore, multiple processors and network
calculations will not speed up these fractal types. In Ultra Fractal 3, rendering these fractal types was
not recommended, but that limitation does not apply anymore. (Formula authors: see the render
setting.)
If you have a processor with HyperThreading, Ultra Fractal will recognize it as a dual processor and
split up its calculations accordingly. In most cases, this will result in a modest speed improvement.
Otherwise, you can force Ultra Fractal to use just one processor.
Open the Options dialog and go to the Fractal tab. In the Advanced calculation options area, the
Minimum number of threads option sets the minimum number of threads that Ultra Fractal will
use for a single fractal window. If this is set to 1, calculations will not be subdivided. Typically, this
should be set to the number of processors in your computer.
Ultra Fractal will typically use one thread per layer. If the number of layers is low, extra threads will
be added (subdividing one or more layers) to reach the minimum number of threads setting, which
ensures that all processors are used. However, if there are many layers, this would create a large
number of threads, which would saturate the system.
The Maximum number of threads option limits the number of threads for a fractal window,
making sure that complex fractals will not start an unlimited number of threads. By default, this is
set to four times the number of processors in your computer. If you would like more layers to be
calculated simultaneously, you can increase this setting.
[1] A thread is an independent part of a program that can run on a processor. Each thread can run
on a separate processor. By splitting calculations into multiple threads, Ultra Fractal ensures that
all processors in your computer are used efficiently.
[2] To use IFS and Flame Fractals, you first need to download the set of public formulas from the
online formula database. Select Pixel in mt.ufm as the fractal formula and either Iterated
Function Systems in mt.ucl, or Flame Fractals in enr.ucl as the outside coloring algorithm.
See Also
Fractal windows
Playing animations
122
Gradients
Gradients contain coloring information for fractals. Each layer in a fractal has its own gradient.
Gradients can also be edited and saved independently with a stand-alone gradient editor.
To open the gradient editor associated with a fractal window, click Gradient on the Fractal
menu. This gradient editor can be recognized because it shows the name of the fractal and
the active layer in the title bar. When the gradient is edited, the fractal window immediately
redraws itself to show the new colors.
To open a stand-alone gradient editor, click New on the File menu, and then click Gradient.
The gradient editor provides various views on the gradient. Each view can be collapsed and
expanded by clicking the button on the left of it. There are five views:
Red/Green/Blue
Edits the gradient in the RGB color model
Hue/Saturation/Luminance
Edits the gradient in the HSL color model
Opacity
Edits the transparency of the gradient
Controls
Allows you to fine-tune the selected control point by
entering values manually
Comments
Provides a place to type comments
The rotation slider is placed outside the collapsible views, so it is always visible. It rotates the
123
gradient to change the way the colors are mapped onto the fractal.
Just above the rotation slider is the animation bar, which is normally empty. It shows the
animation keys for animated control points in the gradient. See Animating gradients.
Next: Gradient toolbar
See Also
Tutorial: Learning basic skills
How gradients work
Transparent gradients
Fractal windows
124
Gradient toolbar
The toolbar for the gradient editor contains commands to edit and save the gradient:
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The New button creates a new fractal from scratch. To create a new gradient, click New on the File
menu and then click Gradient. To duplicate the existing gradient, click Duplicate on the File menu.
The Open and Browse buttons open files from disk.
The Save button saves the gradient to disk. See Opening and saving gradients.
The Undo and Redo buttons can undo and redo changes to the gradient.
The Copy and Paste buttons copy gradients to and from the Clipboard. This is useful for copying
gradients between layers or between fractals.
The Fractal button activates the fractal window that owns the gradient editor. This button is not
available with stand-alone gradient editors. Together with the Gradient button next to it, you use
these buttons to switch back and forth between the fractal window and the gradient editor.
The Select Color, Randomize Color, and Eyedropper buttons change the color of the selected
control point. See Editing gradients.
The Insert button adds a new control point. The Delete button removes the selected control point.
The Link Color and Opacity button links and unlinks the color and opacity parts of the gradient. See
Transparent gradients.
The Smooth Curves button controls how curves between control points are interpolated: linearly or
smoothly.
The commands on the toolbar are duplicated on the File, Edit and Gradient pull-down menus. Frequently used
commands are also on the menu that pops up when you right-click inside the gradient editor.
Next: How gradients work
See Also
Keyboard shortcuts for gradient editors
Gradients
125
How gradients work
When Ultra Fractal calculates a fractal, it does not immediately calculate a color for each pixel. Instead, it
calculates an intermediate index value. The index value is a single floating-point number that is returned
by the selected coloring algorithm.
The gradient translates index values to colors. Since only the index values are stored, the colors can be
changed without having to recalculate the fractal. To put it another way, the coloring algorithm defines
the distribution of the colors, the gradient defines the colors themselves.
Here is an example. This is the same fractal with three different gradients, shown below each fractal.
The fractal contains only colors from the gradient. In addition, you can also recognize the color transitions
from the gradient in the fractal. This is because most coloring algorithms, such as the one used here,
create smooth ranges of index values. Note how the gradient wraps around at the endpoints to create
smoothly colored images.
Note that with direct coloring algorithms, the coloring algorithm directly calculates the color of a pixel,
and the gradient is used differently. A direct coloring algorithm can use colors from the gradient, but it is
not limited to the gradient alone.
Next: Editing gradients
See Also
Gradients
126
Editing gradients
The colors in the gradient are edited by dragging the control points. You can use either the
Red/Green/Blue view or the Hue/Saturation/Luminance view. They both edit the same control points,
but with different color models. You can resize the gradient editor for more accurate positioning of
the control points.
Click a control point to select it. Hold down Shift or Ctrl and click to select multiple control points.
Click on the curve background to deselect all control points. To draw a rectangle around control
points to select them, click on the curve background and drag.
Drag a control point to change its color and position. To change only the position or only the color,
hold down Shift while dragging. In the Controls view, you can manually enter the color and position
of the control point for fine-tuning.
Click Insert on the Edit menu, and then click somewhere in the gradient editor to insert a
new control point there. You can also hold down Ctrl and click on the curve background
where you want to insert a new control point.
Click Delete on the Edit menu to delete the selected control point. You can also hold down
Ctrl and click on the selected control point, if no other control points are also selected.
Right-click in the gradient editor and click Select Color to open a dialog box to change the
color of the selected control point. This is an alternative to dragging the control point itself.
Right-click in the gradient editor and click Randomize Color to set the color of the selected
control point to a random value.
Right-click in the gradient editor and click Eyedropper to pick the color of the selected
control point from any open gradient editor or fractal window. Click Eyedropper again to
cancel.
Click Smooth Curves on the Gradient menu to toggle between linear interpolation and
smooth interpolation for the curves. This affects how the gradient is colored between control
points.
Click Undo on the Edit menu to undo the changes you have made. The history list of the
gradient is independent from the fractal history list, but it is reset when undoing changes to
the fractal.
Use the Copy and Paste commands on the Edit menu to copy the gradient to the Clipboard
and paste the gradient on the Clipboard into the editor, replacing the current gradient. This
enables you to copy gradients to other layers, other fractal windows, and to and from standalone gradient editors.
Next: Transparent gradients
See Also
127
Tutorial: Learning basic skills
Tutorial: Working with layers
Keyboard shortcuts for gradient editors
Gradients
Animating gradients
128
Transparent gradients
The gradient defines not only the colors of a layer, but also the transparency. An opacity value is
associated with every color to make it more or less transparent. By default, all opacity values are set
to 255, which makes them completely opaque.
Use the Opacity view to edit the opacity of the gradient. The opacity curve can be edited
independently from the color curves (they do not necessarily share the same control points). To edit
the curve, click on the Opacity view to activate it, and drag the control points, just like when you edit
the color curves. Drag a control point up to make it opaque, drag it down to make it transparent.
The pattern of blocks shows the transparency of the gradient. This pattern is also visible in the
fractal window unless there is a layer below the current layer that is completely opaque, in which
case the underlying layer is shown.
Many gradient commands work only on the active curve or curves. For example, when the opacity
curve is active, the Smooth Curves command (click Smooth Curves on the Gradient menu) will
adjust the curvature of the opacity curve instead of the color curves. Only the active curve shows
control points.
You can link the color curves and the opacity curve so they share the same control points.
To link them, click Link Color and Opacity on the Gradient menu. This will adjust the
opacity curve to give it the same control points as the color curves. You can now edit the
opacity and color curves simultaneously.
Next: Adjusting gradients
See Also
Tutorial: Working with layers
Tutorial: Masking
Layers
Masks
Gradients
129
Adjusting gradients
To edit the gradient, you usually manipulate individual control points. However, there are also
several commands that adjust the entire gradient. These commands will work on the active curves
(color or opacity), or both when they are linked together (see Transparent gradients).
Click Adjust Colors on the Gradient menu to open the Adjust dialog. This dialog allows you
to change the color balance, hue, saturation, brightness, and contrast of the entire gradient.
For example, by moving the Saturation slider in the HSL tab completely to the left, you can
create a grayscale version of the gradient.
Click Randomize on the Gradient menu to randomize the gradient. This fills the gradient
with a random number of control points, all with random colors.
Click Randomize Bright or Randomize Misty for a different selection of colors.
Click Randomize Custom to open a dialog with a variety of options for randomizing the
gradient. Here, you can randomize for example only the positions of the control points, or
choose from specific ranges of values for the colors.
Click Reverse on the Gradient menu to reverse (mirror) the positions of the control points, so the
leftmost point will appear on the right, and the rightmost point on the left.
Click Invert on the Gradient menu to invert the colors or opacity values of the control points. This is
often useful with the opacity curve, to invert what is transparent and what is opaque.
Next: Opening and saving gradients
See Also
Animating gradients
Editing gradients
Gradients
130
Opening and saving gradients
Gradients are saved in gradient files (*.ugr). A gradient file is a plain text file that can contain any
number of gradients, so you can store and organize sets of gradients.
To save a gradient, click Save on the File menu. The Save Gradient browser will open. You
can save the gradient in an existing gradient file or in a new file. Type the name of the file
and the title of the gradient and click Save.
To open a previously saved gradient, click Browse on the File menu. This opens a modeless
browser. Make sure Gradient Files is selected in the toolbar. Select the gradient file that
contains the gradient that you want to open, and then double-click the gradient inside the
file. The gradient will be opened in a new stand-alone gradient editor.
To open a gradient in the active gradient editor, click Replace on the File menu instead.
This is useful if you want to use the saved gradient in a fractal.
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When saving a gradient, you can choose to save only the color or opacity parts of the
gradient with the Save Color and Save Opacity checkboxes.
Another way to open gradients is to click Open on the File menu and select a gradient file. A
modal browser window will open, showing the gradients in the file. Double-click a gradient to
open it.
Palette files in Fractint's MAP format (*.map) can be opened just like other gradient files.
See Also
Browsers
Parameter files
Gradients
131
Fractal formulas
The fractal formula creates the basic shape and form of a fractal. Ultra Fractal comes with a number
of standard formulas that you can use. You can also download additional formulas from the Internet
and even write your own formulas.
Fractal formulas are managed in the Formula tab of the Layer Properties tool window.
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At the top, the title of the fractal formula is shown. Hold the mouse cursor over the title to
see the entry identifier and the file name of the formula.
The Browse button opens a modal browser to select another fractal formula.
The Reload button reloads the fractal formula from disk and recalculates the layer.
The Edit button opens the fractal formula in the formula editor.
The Help button opens the help file for the formula, if one exists.
The More button shows a menu with additional commands.
The calculation settings specify how the fractal should be calculated. See Working with
fractal formulas.
The iteration settings specify how many iterations should be used. See Maximum
iterations.
The formula parameters are additional parameters specific to the selected fractal formula.
See Formula parameters.
Next: Working with fractal formulas
See Also
Quick Start Tutorial
Coloring algorithms
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Transformations
What are fractals?
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Working with fractal formulas
You work with fractal formulas in the Formula tab of the Layer Properties tool window. This tab also
contains global calculation settings for the layer, since these are closely related to the selected
fractal formula.
Fractal formulas are stored in fractal formula files (*.ufm). Each file can contain multiple formulas.
To select a fractal formula, click the Browse button. This opens a modal browser that shows
the formula files and formulas on your computer. Double-click on a formula to select it.
Hold down the Browse button to open a menu with fractal formula presets. See Presets.
Some formulas contain additional help. Click the Help button to open it.
Click the More button to access commands to copy and paste the settings and parameters
on the Formula tab, and to reset all parameters to the default values.
The Formula tab is divided into two panes. The top pane contains global calculation settings.
Drawing Method
Selects how the pixels are calculated.
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Guessing starts with a low-resolution preview, and then
gradually increases the resolution while trying to guess pixels
instead of calculating them. This is the fastest option, but
also the least accurate. When you are working with
animations, use this drawing method for fast animation
previews.
Multi-pass Linear also starts with a low-resolution preview,
but it calculates all pixels instead of guessing them.
One-pass Linear calculates all pixels from top to bottom.
For maximum accuracy, use one of the linear drawing methods.
Periodicity Checking
Specifies the amount of periodicity checking used. Periodicity
checking can greatly enhance the speed at which inside areas are
calculated. Rough is the fastest option, but also the least accurate.
Off turns off periodicity checking completely for the highest accuracy.
Some fractal formulas do not work well with periodicity checking, in
which case you should turn it off. If odd lines or dots appear on the
top of the fractal, this may be the case.
Additional Precision
Specifies how many extra digits of precision should be used for
calculations. See Arbitrary Precision.
The top pane also contains the iteration settings. The bottom pane contains the formula parameters.
These parameters are specific to the selected fractal formula.
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Next: Maximum iterations
See Also
Fractal formulas
Standard fractal formulas
135
Maximum iterations
To calculate a pixel in a fractal, Ultra Fractal iterates the selected fractal formula. It executes it
multiple times, each time using the result from the previous calculation as input.
The formula is iterated until the maximum iteration count is reached, or until the bail-out condition
(specified by the fractal formula) is met. If the bail-out condition is met, the pixel is colored as an
outside pixel. Otherwise, it is colored as an inside pixel.
Sometimes, many iterations are necessary to reach the point where the bail-out condition is satisfied.
If the maximum iteration count is too small, the pixel will be incorrectly colored as an inside pixel
because the bail-out point is not reached. On the other hand, if the iteration count is too large, many
iterations will be performed for the pixels that are inside, and the fractal will be calculated slowly.
The Maximum Iterations setting on the Formula tab of the Layer Properties tool window specifies
the maximum iteration count. To help you find a good value, the Statistics tool window shows a
histogram of the iteration values on its Iterations tab.
This example illustrates the influence of the maximum iterations setting:
Maximum iterations: 20
Maximum iterations: 200
Maximum iterations: 2000
We see the same image three times, with three different values for the maximum number of
iterations. Below each image, the iterations histogram from the Statistics tool window is shown.
The first image clearly suffers from a low value for the maximum iterations setting. By increasing it,
we obtain the second image, which looks much better. Further increasing the value does not change
the image much, so we conclude that 200 is a good value in this case.
Notes
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The histogram can aid you in deciding whether or not you have to change the maximum
iterations value. If most of the iterations end up on the left side (as with the middle image),
you are probably safe. If they are all at the far left side, the value is probably too high (which
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makes the fractal slower to calculate). If there are many iterations on the right side, the
value is too low. Move the mouse pointer over the tool window to see the corresponding
iteration values.
Experiment with the maximum iterations setting to learn how to use it. Sometimes, a (too)
low value can also be artistically pleasing.
By checking the Adjust Automatically checkbox on the Formula tab, Ultra Fractal
automatically adjusts the maximum iterations value when zooming in or out. This can be
helpful, but it is not fool-proof: you may need to adjust the value manually every once in a
while.
Next: Formula parameters
See Also
Fractal formulas
Working with fractal formulas
Inside and outside
137
Formula parameters
The bottom pane on various tabs of the Layer Properties tool window contains parameters that are
specific to the selected transformation, fractal formula, or coloring algorithm. There are eight types
of parameters:
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Complex parameters consist of a real and an imaginary value. They appear as two input
boxes labeled with "(Re)" and "(Im)" after the name of the parameter. Right-click one of the
input boxes to open a menu with additional options.
Floating-point parameters specify a single floating-point value (such as -0.2 or 3.14).
Integer parameters specify an integer value (such as -2 or 3).
Enumerated parameters appear as a drop-down box. They are typically used to select one
of various behaviors, or to choose between a number of options.
Color parameters specify a color and are typically used only by direct coloring algorithms.
They appear as a color swatch. Click it to adjust the color. Right-click it to open a menu with
additional options.
Boolean parameters appear as a checkbox. They are used to turn options on or off.
Class parameters provide a way to extend a formula with additional features. See About
classes.
Image parameters, typically used in coloring algorithms, enable importing external images.
See Using images.
Many formulas require a bit of experimentation with the parameters to learn how to use them. For
new users, it is best to stick to the standard formulas and learn how to use these first.
Some formulas (such as the standard formulas) contain additional help. To access it, click
the Help button.
To copy the formula settings (including parameter values) between layers, click the More
button, and then click Copy or Paste.
To reset all parameters to their default values, click the More button, and then click Reset
Parameters.
In some formulas, such as Orbit Traps, parameters are divided into groups by headings.
You can collapse and expand the heading and the parameters below it by clicking on the arrow
button. Right-click the heading for a menu with commands to collapse and expand all headings.
Notes
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You can horizontally resize the area reserved for parameter labels, for example to make
more space available for long labels. Simply position the mouse cursor just left of a
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parameter input box so it turns into a horizontal resize cursor, and drag this edge to where
you want it to be. Double-click here to reset the label area to the default size.
Many formulas contain help for individual parameters. Make sure the Fractal Mode tool
window is visible and hover the mouse cursor over a parameter to see its help text, if one
exists.
The Explore feature makes it easy to try new parameter values.
If multiple layers or transformations are selected that do not use the same formula, the list
of parameters remains empty.
You can easily copy complex values from one parameter to another. Right-click a complex
parameter and click Copy Complex Value or Paste Complex Value. You can also copy
coordinates between the Location tab and a complex parameter in this way. To copy a color
parameter, right-click it and click Copy or Paste.
Next: Explore
See Also
Animating parameters
Fractal formulas
Working with fractal formulas
139
Explore
You can try new parameter values by typing one after the other, but it is much better to use the
Explore feature. The Explore feature makes experimenting with parameters easier and more fun.
If you click on a parameter to give it the keyboard focus, a small window will pop up below the input
box with two buttons. These invoke the Explore and Eyedropper features.
Click the Explore button to start exploring the parameter.
The Explore window will pop up. It contains a coordinate grid, rulers, and zooming controls.
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Move the mouse cursor over the coordinate grid to try different parameter values. Look at
the Fractal Mode tool window to see a live preview of the active fractal layer with the current
parameter value.
Enter a new value in the range input box, or use the Zoom In and Zoom Out buttons to
decrease or increase the coordinate range.
The rulers show the current coordinates. Drag them around to pan the coordinate grid.
Click inside the coordinate grid to select a new value. The Explore window will close and the new
parameter value will be applied.
The Explore feature works with complex, floating-point, and integer parameters. The picture above
shows the Explore window in complex mode. When exploring floating-point and integer parameters,
the vertical ruler is not included.
Notes
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You can also pan or zoom by dragging the coordinate grid while holding the Ctrl or Shift key,
just like in the fractal window.
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A small circle in the Explore window shows the original value of the parameter that is being
explored.
To cancel without selecting a new parameter value, either close the Explore window, or click
on the explore icon that has appeared in the input box for the parameter that is being
explored.
Another way to start exploring a parameter is by right-clicking it and selecting Explore from
the menu that pops up.
Next: Eyedropper
See Also
Formula parameters
Fractal formulas
Working with fractal formulas
141
Eyedropper
Another tool to choose new parameter values is the Eyedropper feature. It is similar to the Explore
feature, but it selects parameter values from the coordinates in the fractal window, instead of using a
separate coordinate grid. This is useful if the fractal coordinates have a relationship with the
parameter that you are working with.
For example, to choose new values for the Julia Seed parameter of a Julia set, open a separate
fractal window with the Mandelbrot set, and use the Eyedropper feature to pick values from the
Mandelbrot fractal, as an alternative for Switch mode.
If you click on a parameter to give it the keyboard focus, a small window will pop up below the input
box with two buttons. These invoke the Explore and Eyedropper features.
Click the Eyedropper button to start eyedropper mode.
As you move the mouse cursor over a fractal window, you see the fractal coordinates for the point
under the mouse cursor in the input box for the parameter that is in eyedropper mode. You can
select coordinates from any fractal window, not just the active window.
Look at the Fractal Mode tool window for a live preview of the active fractal layer with the current
parameter value. Simply click inside the fractal window to select the new parameter value.
The Eyedropper feature works with complex, floating-point, integer, and color parameters. With
floating-point and integer parameters, only the real part of the fractal coordinates is used.
To use the eyedropper with color parameters, right-click the color parameter and click Eyedropper.
You can select colors from any fractal window or gradient editor.
Notes
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To cancel without selecting a new parameter value, click on the eyedropper icon that has
appeared in the input box for the parameter that is in eyedropper mode.
Another way to start the eyedropper is by right-clicking a parameter and selecting
Eyedropper from the menu that pops up.
Next: Presets
See Also
Explore
Formula parameters
Fractal formulas
Working with fractal formulas
142
Presets
As you work with formulas in Ultra Fractal, you will often use the same combinations of formulas and
parameters to achieve certain effects. You can save the combination of a formula and parameters as
a preset for quick access in the future.
To open a saved formula preset, click and hold down the Browse button until a menu with
presets appears. Simply click a preset to load it.
To save and organize presets, click Define on the presets menu. This opens the Edit Presets dialog.
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Click Add Current to save the current settings as a new preset.
Click Delete to delete the selected preset.
Click Rename to rename the selected preset. You can also click a preset in the list twice, or
press F2.
Use the Move Up and Move Down buttons to reorder presets, or just drag them around in
the list.
Click OK to apply your changes.
Besides fractal formulas, there are also presets for coloring algorithms, transformations, and layers.
To access the transformation presets, click and hold down the Add button in the Mapping tab. To
access the layer presets, click and hold down the Add button in the Layers tab of the Fractal
Properties tool window.
Presets are saved in files with the .ups file extension in the Ultra Fractal system folder,
which is displayed on the Folder tab of the Options dialog. You might want to include these
files when you make a backup of your fractal documents.
Next: Arbitrary precision
See Also
Fractal formulas
Working with fractal formulas
Parameter files
143
Arbitrary precision
Ultra Fractal can perform fractal calculations with almost any desired precision. This enables you to
zoom as deep as you want, without hitting a precision limit. This is called arbitrary precision or deep
zooming.
Three types of precision are available:
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Double is the fastest and the least precise method. It supports magnifications up to about
1010 (1E10, or 10 billion). It has a precision of 15-16 decimals.
Extended is slightly more precise and a little slower, supporting magnifications up to about
1016. It has a precision of 19-20 decimals.
Arbitrary is much slower, but it supports magnifications up to 104000. Its precision can be
scaled from 20 to 10,000 decimals.
Ultra Fractal automatically selects the best precision type, depending on the current magnification
and the selected fractal formula, transformations, and coloring algorithms. It calculates the number
of decimals required and selects the fastest precision type that can support it.
You can verify the number of decimals required and the selected precision type in the General tab of
the Statistics tool window.
Sometimes, you may want to adjust the number of decimals to force Ultra Fractal to use a different
precision type, or to change the number of decimals used with the Arbitrary precision type. The
Additional Precision input box on the Formula tab of the Layer Properties tool window allows you
to do this.
The value in the Additional Precision input box is added to the default number of decimals required.
Positive values will increase the precision; negative values will decrease it. Keep an eye on the
Statistics tool window to see the effect.
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It is not recommended to try and use the additional precision to achieve artistic effects, since
they would rely on artefacts in the current implementation, and might be broken by future
versions.
Some older formulas rely on the Extended precision that was always used by Ultra Fractal 2.
In this case, you can adjust the additional precision (looking at the Statistics tool window)
until the Extended precision type is used.
To force Ultra Fractal to always or never use Arbitrary precision, select the desired option in
the Use arbitrary precision area on the Fractal tab of the Options dialog.
Next: Public formulas
See Also
Fractal formulas
144
Public formulas
Ultra Fractal comes with a set of standard fractal formulas, transformations, coloring algorithms and
classes. They are easy to use and well documented. However, when you get more experienced, you
will want to work with more different formulas.
Most of the custom formulas and classes written for Ultra Fractal are available through a public
formula database on the Internet (formulas.ultrafractal.com). Here, you can download a complete
set of formulas, browse the collection, and add your own formulas.
You can download formulas and classes from the database from within Ultra Fractal. This will
automatically download new and updated files and install them appropriately.
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To start updating your collection of public formulas, click Update Public Formulas on the
Options menu. You can select what to download: the weekly or monthly update, or the full
collection. Ultra Fractal will automatically select the most appropriate option depending on
how long ago you last updated the formulas.
The downloaded files will be installed in the Public formulas folder.
Notes
You are free to organize the public formulas in subfolders in the Public formulas folder, for
example to put files that you rarely use in a separate folder. The files will still be updated
correctly.
The formula database also contains text files with documentation and parameter files with
examples. These are copied to the Public formulas folder as well.
If you have a dial-up connection, make sure you are connected to the Internet before
updating your formulas. Otherwise, Ultra Fractal might not be able to connect to the formula
database.
When opening a parameter set that uses formulas that cannot be found, you can directly
download the file from the formula database.
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How are the public formulas installed?
The formulas will be installed according to the following rules:
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If a formula file already exists in the Public formulas folder or in a subfolder, it will be
overwritten. If the existing file is newer than the downloaded file, you will be prompted for
confirmation.
If a formula file does not exist yet, it will be created in the Public formulas folder.
If a formula file already exists outside the Public formulas folder, it will not be updated or
overwritten. These files are listed as skipped. If you are a formula author, you can thus
avoid overwriting your own files when updating the formulas by placing them in the
Formulas\My Formulas folder instead of in Formulas\Public.
When all files are downloaded and installed, a short summary of the changes is shown. Details can
be found in the Update.log file created in the Public formulas folder.
By default, the location of the Public formulas folder is Documents\Ultra Fractal 5\Formulas\Public.
It is always located under the main Formulas folder. You can change its location in the Folder tab of
the Options dialog.
Next: Standard formulas
145
See Also
Formula ratings
Transformations
Fractal formulas
Coloring algorithms
146
Standard fractal formulas
Ultra Fractal comes with a set of standard fractal formulas. They are located in the file Standard.ufm
in the Formulas folder. It contains the following formulas:
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Embossed (Julia, Mandelbrot, Newton)
Generic Formula
Julia
Julia (Built-in)
Lambda (Julia, Mandelbrot)
Magnet 1 and 2 (Julia, Mandelbrot)
Mandelbrot
Mandelbrot (Built-in)
Newton
Nova (Julia, Mandelbrot)
Phoenix (Julia, Mandelbrot)
Pixel
Slope (Julia, Mandelbrot, Newton)
All standard fractal formulas are also implemented as fractal formula classes in Standard.ulb. This
makes it possible to use them with Generic Formula or in other formulas that accept fractal formula
classes. See About classes and Example 1 - Formula classes for more information.
See Also
Standard transformations
Standard coloring algorithms
Fractal formulas
Public formulas
147
Embossed (Julia, Mandelbrot, Newton)
The Embossed fractal formulas are modifications of the classic
Mandelbrot, Julia, and Newton fractals that create 3D bevel effects with
contour lines. They are available as fractal formulas in Standard.ufm
and as a fractal formula class in Standard.ulb.
In class form, Embossed uses a class parameter to select which fractal
formula to use, so it is not just limited to Mandelbrot, Julia or Newton
fractal types. See Example 1 - Formula classes for more information.
Embossed should be combined with the Emboss coloring algorithm. This coloring algorithm correctly
translates the results from the Embossed fractal formulas to colors in the gradient.
For best results, use a black-to-white gradient such as Emboss in Standard.ugr. This will create a
grayscale image with shaded contour lines. You can then combine this with other layers to add colors
while retaining the 3D effect. For the merge mode of the layer with the Embossed formula, try Soft
Light or Hard Light.
The following parameters are provided:
Fractal Formula
Selects the fractal formula to use for the embossing effect. (Class version of
Embossed only.)
Emboss Type
Specifies what kind of information from the fractal calculations is used to
create the embossing effect. This changes the shape and place of the
contour lines.
Light Angle
This is the angle of the apparent light source, in degrees. The default value
0 corresponds to light from above. Positive values rotate the light source in
clockwise direction.
Contour Size
Specifies the relative size of the contour lines. When zooming in, the size in
pixels of the contour lines appears to stay the same.
For the non-class version of the Embossed fractal formulas, the other parameters are described in
the topics for the regular (non-Embossed) formulas.
Note: When rendering embossed fractals, use non-adaptive anti-aliasing to ensure that the contour
lines are anti-aliased correctly, and make sure the Force Linear drawing method option is checked.
See Also
Slope (Julia, Mandelbrot, Newton)
Standard formulas
148
Generic Formula
Generic Formula is a skeleton fractal formula that lets a fractal formula
class do the actual work. All fractal formulas in Standard.ufm are also
implemented as fractal formula classes. You can select any of these as
the fractal formula class to be used together with Generic Formula.
The Fractal Formula class parameter sets the fractal formula class to
be used. By default, the Mandelbrot class from Standard.ulb is selected.
An example of using Generic Formula is given in Example 1 - Formula classes.
See Also
About classes
Standard fractal formulas
Standard classes
149
Julia
Julia sets are closely related to the well-known Mandelbrot set. In fact,
the Mandelbrot set is a map of Julia sets. For each point in the
Mandelbrot set, there exists a unique Julia set.
Use the Switch feature to select a Julia set by moving the mouse cursor
over a Mandelbrot fractal. The most interesting Julia sets are found at
points close to the edge, where the colors change quickly.
Julia sets are strictly self-similar and less complex than the Mandelbrot set. Still, they can be
strikingly beautiful, and they are certainly very interesting to explore.
Julia is available as a fractal formula in Standard.ufm and as a fractal formula class in Standard.ulb.
The following parameters are provided:
Julia seed
This parameter specifies the point in the Mandelbrot set that corresponds to
the current Julia set. It defines the shape and behavior of the Julia set. Use
the Switch feature to select good values.
Specifies the exponent. The default value is (2, 0), resulting in the classic
equation.
z = z2 + c
Power
Try (3, 0) and (4, 0) and so on to increase the symmetry order. Non-integer
values for the real part of the exponent or non-zero values for the imaginary
part will distort the fractal.
Specifies the magnitude of z that will cause the formula to stop iterating. To
obtain "true" Julia sets, this should be set to 4 or larger. Larger values tend to
smooth the outside areas.
Bailout value
Some coloring algorithms require specific bail-out values for good results.
Note: The Julia formula is also available as a more efficient built-in formula with fewer options. See
Julia (Built-in).
See Also
Lambda (Julia, Mandelbrot)
Julia sets
Standard formulas
150
Julia (Built-in)
This is a built-in and faster version of the Julia formula. Julia sets are
closely related to the well-known Mandelbrot set. In fact, the Mandelbrot
set is a map of Julia sets. For each point in the Mandelbrot set, there
exists a unique Julia set.
Use the Switch feature to select a Julia set by moving the mouse cursor
over a Mandelbrot fractal. The most interesting Julia sets are found at
points close to the edge, where the colors change quickly.
Julia sets are strictly self-similar and less complex than the Mandelbrot set. Still, they can be
strikingly beautiful, and they are certainly very interesting to explore.
The formula provides the following parameters:
Julia seed
This parameter specifies the point in the Mandelbrot set that corresponds to
the current Julia set. It defines the shape and behavior of the Julia set. Use
the Switch feature to select good values.
Specifies the magnitude of z that will cause the formula to stop iterating. To
obtain "true" Julia sets, this should be set to 4 or larger. Larger values tend to
smooth the outside areas.
Bailout value
Some coloring algorithms require specific bail-out values for good results.
Note: The Julia formula is also available as a normal formula that is less efficient, but offers more
options. See Julia.
See Also
Julia sets
Standard formulas
151
Lambda (Julia, Mandelbrot)
The Lambda formula is an alternative version of the equation for Julia
fractals. While it is capable of creating the same Julia sets, the
corresponding Mandelbrot version looks different.
Both Mandelbrot and Julia versions of the Lambda fractal are available
as fractal formulas in Standard.ufm and as fractal formula classes in
Standard.ulb.
Because the Mandelbrot version is a map of Julia sets, this allows you to find Julia sets with the
Switch feature in a different way than with the usual Mandelbrot set. It is easier to find good spirals
and other interesting Julia sets.
The formulas provide the following parameters:
For the standard Lambda Mandelbrot set, this should be set to (0.5, 0). Other
values create distorted shapes that can be interesting, but they are usually
not as well-formed as the standard set.
Start Value
(Mandelbrot only)
Julia Seed
(Julia only)
For well-formed sets, the real value should be set to 1 divided by the real
value of the exponent. For example, use (0.25, 0) if Exponent is set to (4, 0).
This parameter specifies the point in the Mandelbrot version that corresponds
to the current Julia set. It defines the shape and behavior of the Julia set. Use
the Switch feature to select good values.
Specifies the exponent. The default value is (2, 0), resulting in the classic
equation.
c * z * (1 - z)
Exponent
Try (3, 0) and (4, 0) and so on to increase the complexity of the fractal. Noninteger values for the real part of the exponent will interpolate between these
well-formed sets. If the imaginary part is not zero, the fractal will be further
distorted.
Specifies the magnitude of z that will cause the formula to stop iterating. To
obtain well-formed fractals, this should be set to 4 or larger. Larger values
tend to smooth the outside areas.
Bailout
Some coloring algorithms require specific bail-out values for good results.
See Also
Julia sets
Standard formulas
152
Magnet 1 and 2 (Julia, Mandelbrot)
The magnetic fractal types are created by a formula that models the
way magnets behave under high temperatures. This leads to fractal
pictures that are similar to the classic Mandelbrot and Julia sets, but
with more complex patterns and numerous Mandelbrot set miniatures.
There are two common magnetic fractal types. Type 2 is more complex
than type 1. Both types are available as Mandelbrot and Julia versions,
so you can use the Mandelbrot version as a map to switch to the
corresponding Julia fractals.
Both Mandelbrot and Julia versions of the Magnet fractals are available as fractal formulas in
Standard.ufm and as fractal formula classes in Standard.ulb.
The formulas provide the following parameters:
Perturbation
(Mandelbrot only)
For the standard fractals, this should be set to (0, 0). Other values create
distorted shapes that can be interesting, but they are usually not as wellformed.
Parameter
(Julia only)
This parameter specifies the point in the Mandelbrot version that corresponds
to the current Julia set. It defines the shape and behavior of the Julia set. Use
the Switch feature to select good values.
Bailout value
Specifies the magnitude of z that will cause the formula to stop iterating. Use
a value above 30 to obtain well-formed fractals.
Convergent
bailout value
Specifies the minimum difference between subsequent z values at which the
formula will stop iterating. Smaller values give more accurate results at the
expense of calculation time.
See Also
Standard formulas
153
Mandelbrot
The Mandelbrot set is the most well-known fractal type. Although it is
calculated by a simple formula, it is incredibly complex. As you zoom in,
more and more ever-changing detail becomes visible, such as little
"baby" Mandelbrot sets and all kinds of spirals.
Because the Mandelbrot set lends itself well to basic zooming and
exploring, it is a good starting point if you are new to fractals. It is
available as a fractal formula in Standard.ufm and as a fractal formula
class in Standard.ulb.
The formula provides the following parameters:
Starting point
For the standard Mandelbrot set, this should be set to (0, 0). Other values
create distorted shapes that can be interesting, but they are usually not as
well-formed as the standard set. Try (0, -0.6), for example.
Specifies the exponent. The default value is (2, 0), resulting in the classic
equation.
z = z2 + c
Power
Try (3, 0) and (4, 0) and so on to increase the number of main "buds". Noninteger values for the real part of the exponent will interpolate between these
well-formed sets. If the imaginary part is not zero, the fractal will be further
distorted.
Specifies the magnitude of z that will cause the formula to stop iterating. To
obtain the "true" Mandelbrot set, this should be set to 4 or larger. Larger
values tend to smooth the outside areas.
Bailout value
With the Basic coloring algorithm and the Color Density set to 4, try the bailout values 4 and then 16 to see the difference.
Some coloring algorithms require specific bail-out values for good results.
Notes
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The Mandelbrot set is also available as a more efficient built-in formula with fewer options.
See Mandelbrot (Built-in).
The Mandelbrot set also acts as a map of Julia sets. Use Switch mode to switch to related
Julia sets.
See Also
The Mandelbrot set
Standard formulas
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Mandelbrot (Built-in)
This is a built-in and faster version of the standard Mandelbrot set: the
most well-known fractal type. Although it is calculated by a simple
formula, it is incredibly complex. As you zoom in, more and more everchanging detail becomes visible, such as little "baby" Mandelbrot sets
and all kinds of spirals.
Because the Mandelbrot set lends itself well to basic zooming and
exploring, it is a good starting point if you are new to fractals.
The formula provides the following parameters:
Starting point
For the standard Mandelbrot set, this should be set to (0, 0). Other values
create distorted shapes that can be interesting, but they are usually not as
well-formed as the standard set. Try (0, -0.6), for example.
Specifies the magnitude of z that will cause the formula to stop iterating. To
obtain the "true" Mandelbrot set, this should be set to 4 or larger. Larger
values tend to smooth the outside areas.
Bailout value
With the Basic coloring algorithm and the Color Density set to 4, try the bailout values 4 and then 16 to see the difference.
Some coloring algorithms require specific bail-out values for good results.
Notes
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There is also a version of the Mandelbrot set as a normal formula (not built-in). Although it is
less efficient, it offers more options, and it is better at handling very large bail-out values.
See Mandelbrot.
The Mandelbrot set also acts as a map of Julia sets. Use Switch mode to switch to related
Julia sets.
See Also
The Mandelbrot set
Standard formulas
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Newton
The Newton fractal is generated by Newton's method for solving
polynomial equations. Different equations are available by changing the
parameters. It is available as a fractal formula in Standard.ufm and as a
fractal formula class in Standard.ulb.
This is a simple and attractive fractal type. Newton fractals are strictly
self-similar, so they are not very interesting zooming subjects. Instead,
try a few different coloring algorithms to decorate them in various ways.
The formula provides the following parameters:
Specifies the exponent of the equation to be solved. The default value is (3,
0), resulting in the equation:
z3 + Root
Exponent
Try (4, 0), (5, 0) and so on to increase the symmetry order. Non-integer
values for the real part of the exponent will interpolate between these. If the
imaginary part is not zero, the fractal will be further distorted.
Root
Specifies the root of the equation. This tends to rotate and magnify the fractal.
Bailout value
Specifies the minimum difference between subsequent z values at which the
formula will stop iterating. Smaller values give more accurate results at the
expense of calculation time.
See Also
Nova (Julia)
Standard formulas
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Nova (Julia, Mandelbrot)
The Nova fractal is a modified Newton fractal. The Julia version can be
used as a normal Newton fractal, but there are all kinds of other
possibilities with intriguing spirals.
Both Mandelbrot and Julia versions of the Nova fractal are available as
fractal formulas in Standard.ufm and as fractal formula classes in
Standard.ulb.
Use the Nova (Mandelbrot) formula to switch to interesting Nova (Julia) sets. The standard Newton
fractals can be found in the empty circle to the right.
The formulas provide the following parameters:
Start Value
(Mandelbrot only)
For well-formed fractals, this should be set to (1, 0). Other values create
distorted shapes that can be interesting, but they are usually not as wellformed.
Julia Seed
(Julia only)
This parameter specifies the point in the Mandelbrot version that corresponds
to the current Julia version. It defines the shape and behavior of the fractal.
Use the Switch feature to select good values.
Exponent
Increase the real value of the exponent to create more complex fractals. Noninteger real values and non-zero imaginary values create irregular fractals.
Bailout
Specifies the magnitude of z at which the formula will stop iterating. Since z
converges to a fixed value, smaller values will give more detailed images.
Relaxation
This can be used to influence the convergence of the fractal. Changing this
parameter will twist and transform the fractal.
See Also
Standard formulas
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Phoenix (Julia, Mandelbrot)
The Phoenix fractal is a modification of the classic Mandelbrot and Julia
sets. The Phoenix (Julia) type is particularly interesting, with beautiful
shapes and lots of spirals.
Use the Phoenix (Mandelbrot) formula to switch to interesting Phoenix
(Julia) sets. Both versions are available as fractal formulas in
Standard.ufm and as fractal formula classes in Standard.ulb.
The formulas provide the following parameters:
Start Value
(Mandelbrot only)
For well-formed fractals, this should be set to (0, 0). Other values create
distorted shapes that can be interesting, but they are usually not as wellformed.
Julia Seed
(Julia only)
This parameter specifies the point in the Mandelbrot version that corresponds
to the current Julia version. It defines the shape and behavior of the fractal.
Use the Switch feature to select good values.
Exponent 1
Increase the real value of the exponent to create more complex fractals with
more symmetry. Non-integer real values and non-zero imaginary values
create irregular fractals.
Exponent 2
By default, this is set to (0, 0). Use other values to create more complex,
twisted fractals.
Distortion
Sets how strong the effect of the previous iteration is upon the current
iteration. Set this to (0, 0) to obtain standard Mandelbrot and Julia sets.
Bailout
Specifies the magnitude of z at which the formula will stop iterating. Higher
values will give smoother images with more detail.
See Also
Standard formulas
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Pixel
The Pixel fractal formula is a simple stub formula that marks all pixels in
the layer as outside. This gives exclusive control over the layer to the
coloring algorithm selected on the Outside tab of the Layer Properties
tool window.
Combined with a direct coloring algorithm such as the standard Image
coloring algorithm, this makes it possible to import images, as shown
here. See Using images for more information.
Pixel is available as a fractal formula in Standard.ufm and as a fractal formula class in Standard.ulb.
See Also
Standard formulas
Image coloring algorithm
Using images
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Slope (Julia, Mandelbrot, Newton)
The Slope formulas are modifications of the classic Mandelbrot, Julia,
and Newton fractals that can create various 3D lighting effects. They are
available as fractal formulas in Standard.ufm and as a fractal formula
class in Standard.ulb.
In class form, Slope uses a class parameter to select which fractal
formula to use, so it is not just limited to Mandelbrot, Julia or Newton
fractal types. See Example 1 - Formula classes for more information.
Slope should be combined with the Lighting coloring algorithm. For each pixel, the Slope formula
calculates a "height" value that is passed to Lighting, which performes the final lighting calculations.
For best results, use a black-to-white gradient such as Lighting in Standard.ugr. This will create a
grayscale image with highlights and shadows. You can then combine this with other layers to add
colors while retaining the 3D effect. For the merge mode of the layer with the Slope formula, try Soft
Light or Hard Light.
The following parameters are provided:
Fractal Formula
Orbit Separation
Height Value
Height Transfer
Height Pre-Scale
Height Post-Scale
Every Iteration
Selects the fractal formula to use for the lighting effect. (Class version of
Slope only.)
To determine proper lighting for a particular point, the Slope formulas
test two orbits that are close together. This parameter specifies how
close they should be. Smaller values give better results, especially for
zoomed-in images. Avoid to use values that are too small for the current
precision range.
Specifies how the apparent height of each pixel will be calculated.
Smooth images can be obtained with potential and distance
estimator. The other options will produce images with sharper edges.
This function will be applied to the height value before calculating the
slope. It can be used to reduce (log) or exaggerate (exp) certain
ranges of height values. The default linear option will not change the
height value.
Scales the height value before it is processed by the transfer function.
Scales the height value further after it has been processed by the
transfer function. When zooming in, you should reduce this to make
sure the highlights and shadows do not become too large.
If selected, the height value is calculated every iteration, which is much
slower. This is only necessary if you are combining the Slope formula
with a coloring algorithm that processes every iteration, such as Orbit
Traps. The normal Lighting algorithm does not need this option.
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For the non-class version of the Slope fractal formulas, the other parameters are described in the
topics for the regular (non-Slope) formulas.
See Also
Embossed (Julia, Mandelbrot, Newton)
Standard formulas
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Coloring algorithms
Coloring algorithms define how fractals are colored. The fractal formula creates the basic shape of
the fractal, and coloring algorithms provide ways to color that shape. This gives you the flexibility to
freely combine coloring algorithms with any fractal formula.
Coloring algorithms are managed in the Inside and Outside tabs of the Layer Properties tool window.
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At the top, the title of the coloring algorithm is shown. Hold the mouse cursor over the title
to see the entry identifier and the file name of the coloring algorithm.
The Browse button opens a modal browser to select another coloring algorithm.
The Reload button reloads the coloring algorithm from disk and recalculates the layer.
The Edit button opens the coloring algorithm in the formula editor.
The Help button opens the help file for the coloring algorithm, if one exists.
The More button shows a menu with additional commands.
The coloring settings specify how the information from the coloring algorithm must be
interpreted to color the fractal. See Coloring settings.
The formula parameters are additional parameters specific to the selected coloring
algorithm. See Formula parameters.
Next: Inside and outside
See Also
Quick Start Tutorial
Using images
Standard coloring algorithms
Fractal formulas
Transformations
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Inside and outside
To calculate a pixel in a fractal, Ultra Fractal iterates the fractal formula selected in the Formula tab
of the Layer Properties tool window. The formula is executed multiple times, each time using the
result from the previous calculation as input.
The formula is iterated until the maximum iteration count (set in the Formula tab) is reached, or until
the bail-out condition (specified by the fractal formula) is met. If the bail-out condition is met, the
pixel is colored as an outside pixel. Otherwise, it is colored as an inside pixel.
Most classic fractal types, such as the Mandelbrot set, are actually a set of points. A pixel can either
be inside or outside the set. If a pixel is inside, it belongs to the Mandelbrot set, for example.
In this image of the Mandelbrot set, the inside area is black. The
outside area is colored according to the number of iterations
required to meet the bail-out condition.
By iterating the fractal formula, Ultra Fractal decides whether a pixel is inside or outside the set. The
pixels that are inside are colored according to the settings in the Inside tab of the Layer Properties
tool window. The pixels that are outside are colored according to the settings in the Outside tab.
The Inside and Outside tabs are identical and provide the same options and settings. Since the
outside area is usually the most interesting area, you will probably use the Outside tab more often.
Notes
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Some coloring algorithms can only be used in the Inside tab, or only in the Outside tab.
Some fractal formulas can change the meaning of inside and outside areas. For example,
they can be intended to work together with a special outside coloring algorithm, and ignore
the settings for inside areas. This is usually noted in the comments at the top of the formula.
Next: Working with coloring algorithms
See Also
Maximum iterations
Coloring algorithms
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Working with coloring algorithms
You work with coloring algorithms in the Inside and Outside tabs of the Layer Properties tool window.
These tabs select the inside and outside coloring algorithms and contain additional coloring settings.
Coloring algorithms are stored in coloring algorithm files (*.ucl). Each file can contain multiple
coloring algorithms.
To select a coloring algorithm, click the Browse button. This opens a modal browser that
shows the coloring algorithm files on your computer and the coloring algorithms that they
contain. Double-click on a coloring algorithm to select it.
Hold down the Browse button to open a menu with coloring algorithms presets. See Presets.
Some coloring algorithms contain additional help. Click the Help button to open it.
Click the More button to access commands to copy and paste the settings and parameters
on the Inside or Outside tab, and to reset all parameters to the default values.
Coloring algorithms interpret the calculations performed by the fractal formula selected in the
Formula tab and visualize parts of these calculations. Each coloring algorithm uses the information
from the calculations in a different way.
Coloring algorithms do not directly calculate colors (except for direct coloring algorithms). Instead,
they produce a floating-point index value that is converted to a color by the gradient.
Typically, the index value 0 produces the left-most color in the gradient, and 0.5 produces the color
in the middle. The index value usually wraps around, so 1 produces the left-most color again. The
coloring settings in the Inside and Outside tabs can be used to tweak this.
Next: Using images
See Also
Coloring algorithms
Standard coloring algorithms
How gradients work
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Using images
Image import in Ultra Fractal works via image parameters in formulas, typically coloring algorithms.
This lets you do much more with imported images than just adding them as a separate layer.
However, it also might make it a little less obvious how to use them.
As a starting point, let's load an image such that it fills the entire layer.
First, use the browser to open the Default parameter set in Examples.upr.
Click the Browse button in the Formula tab of the Layer Properties tool window to select the
Pixel formula in Standard.ufm.
Go to the Outside tab in the Layer Properties tool window, and click the Browse button here
to select the Image coloring algorithm in Standard.ucl.
The Image coloring algorithm contains a single image parameter. It fills the entire layer with the
selected image. Currently, no image is selected, so the image parameter shows up as a rectangular
box with the text (Empty).
Click the Open button to select an image on your computer, for example the Rice.jpg image
that comes with Ultra Fractal. Hold down the Open button to open a menu with the option to
clear the image.
The image parameter now shows a preview of the selected image:
In the fractal window, the image is now shown, but it is moved slightly to the right. This occurs
because the location of the layer is still set to the default Mandelbrot location.
On the Location tab of the Layer Properties tool window, click the Reset Location button to
reset the location to the default for the currently loaded Pixel formula.
Next: Combining fractals with images
See Also
Coloring algorithms
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Image coloring algorithm
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Combining fractals with images
Tip: This example assumes that you are familiar with formulas that use classes, as explained in the
Classes chapter.
As explained in Using images, you can do more with image import in Ultra Fractal than just adding
images as a separate layer. Let's try a different way of importing images.
Again, use the browser to open the Default parameter set in Examples.upr.
This time, we're going to use a Julia fractal. Click the Browse button in the Formula tab of
the Layer Properties tool window to select Julia in Standard.ufm.
To make the fractal more interesting, locate the Julia seed parameter and enter -0.6 for
the (Re) part, and 0.7 for the (Im) part. (Tip: Normally you would use Switch mode to find
values such as these.)
On the Location tab of the Layer Properties tool window, click the Reset Location button to
reset the location to the default for the currently loaded Julia formula.
Go to the Outside tab in the Layer Properties tool window, and click the Browse button here
to select Generic Coloring (Direct) in Standard.ucl.
The Generic Coloring (Direct) coloring algorithm contains the Direct Orbit Traps class by default,
which is perfect for our purpose.
Locate the Color Trap class parameter (currently set to Trap Shape Wrapper) and click the
Browse button next to it. Navigate to the common.ulb file in the Public folder and select the
Image Trap class.
Observe that the Image Trap class contains an image parameter, which is currently empty.
Click the Open button next to it, and select the Ultra Fractal.png image that comes with
Ultra Fractal.
The fractal now fills itself with the Ultra Fractal text from this image, but the image is rotated and
transformed according to the structure of the fractal! Try zooming in to see that the text is repeated
infinitely. It's a true fractal, but using texture from an image that you choose. This works very well if
the image contains transparent areas, which is possible with the PNG image format.
This is just a simple example, but the parameters for the Direct Orbit Traps algorithm let you take
this much further, so feel free to experiment. Also, in the public formula library, you will find more
coloring algorithms that let you use images to color the fractal structure.
Notes
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Ultra Fractal imports JPEG, PNG, and BMP images. Only 24-bit or 32-bit BMP images are
supported. Interlaced PNG files are not supported. The alpha channel from PNG files or 32bit BMP files will be treated as transparency information for the image.
When selecting an image, by default Ultra Fractal starts in the Images folder inside the main
Ultra Fractal documents folder. It is recommended to keep the images that you use with your
fractals here. You can change the location of the Images folder in the Folders tab of the
Options dialog.
When saving fractals or parameter sets, Ultra Fractal stores only a reference to the image
used. When you re-open the fractal or parameter set, the Images folder is automatically
searched for the image that is needed. Only if the image cannot be found, Ultra Fractal will
ask you to locate the image.
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You can write your own formulas that use imported images. See Image parameters.
Next: Coloring settings
See Also
Coloring algorithms
Example 2 - Orbit trap classes
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Coloring settings
The Inside and Outside tabs of the Layer Properties tool window select the inside and outside
coloring algorithms. They also contain additional coloring settings.
These coloring settings specify how the index value returned by the selected coloring algorithm is
interpreted by the gradient.
Color Density
Specifies how quickly the colors in the gradient follow each other.
Values larger than 1 increase the color density. Values below 1
decrease the color density. The color density must be larger than 0.
The index value is multiplied by the color density.
Transfer Function
Selects a transfer function that translates the index value, multiplied
by the color density value, to an entry in the gradient.
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None returns the solid color, ignoring the coloring algorithm.
Linear directly returns the index value.
Sqr squares the index value. When the index value
increases, the color density appears to increase as well.
Sqrt returns the square root of the index value. This
decreases the apparent color density as the index value
increases.
Cube cubes the index value. The color density increases
faster than when using Sqr.
CubeRoot returns the cubed root of the index value. The
color density decreases faster than when using Sqrt.
Log returns the natural logarithm of the index value. The
color density decreases even faster than when using
CubeRoot.
Exp calculates eindex. The color density increases even faster
than when using Cube.
Sin returns the sine of the index value. The result never
exceeds -1...1 and it repeats itself when the index value
increases.
ArcTan returns the inverse tangent of the index value. The
result approaches ½ pi when the index value becomes very
high
Solid Color
Specifies the solid color, which can be used for special purposes. See
Solid color.
Gradient Offset
Specifies an optional offset in the gradient. This value is added to the
index value after applying the Transfer function. Since the gradient
contains 400 entries, the offset value can range from 0 to 399.
You can achieve the same effect by rotating the gradient, but the
offset can be specified for Inside and Outside coloring algorithms
separately.
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Repeat Gradient
Specifies if the gradient must be repeated. When checked, the index
value will wrap around when it reaches 1. So, index values of 0, 1, 2,
and 3 all map to the same gradient index. Otherwise, the index value
is limited to 1, so all colors in the gradient are only used once.
Next: Solid color
See Also
Coloring algorithms
Working with coloring algorithms
Gradients
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Solid color
In the Inside and Outside tabs of the Layer Properties tool window, you can specify a solid color. The
solid color can be used by coloring algorithms for special purposes.
To change the solid color, click on the Solid Color swatch in the Inside or Outside tab. By default, it
is set to black, but you can choose any color. You can also change the opacity. By setting the opacity
to 0, the solid color and thus the areas colored with the solid color will become transparent, so the
lower layers will become visible.
By setting the Transfer function to None, the entire inside or outside area is filled with the solid
color. This is useful if you do not want to use a coloring algorithm for that area. If you use a
transparent solid color, the area will become transparent.
For example, you can use this if you want to color the inside area with a different gradient. Duplicate
the layer and make the inside solid color in the top layer transparent. Now, you can change the
gradient for the lower layer. Only the inside area of the lower layer, and the outside area of the top
layer will be visible.
Notes
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If you make the solid color transparent, layer transparency will be enabled automatically.
See Transparent layers.
Setting the Transfer function to None will not disable the coloring algorithm. For maximum
efficiency, make sure the None coloring algorithm is selected as well.
Next: Direct coloring algorithms
See Also
Coloring algorithms
Solid color (transformations)
172
Direct coloring algorithms
Normal coloring algorithms return an index value that is looked up in the gradient to produce a color
for each pixel. This enables you to easily change the colors by editing the gradient. On the other
hand, it limits the colors that can appear in the layer to the colors available in the gradient.
Unlike normal coloring algorithms, direct coloring algorithms directly return a color for each pixel.
They are more powerful because they can return any desired color, and perform sophisticated
merging operations internally.
Direct coloring algorithms can access the gradient and use its colors, but they are not limited to
those colors. Because of this flexibility, editing the gradient will cause the layer to be recalculated.
You can still use the coloring settings (such as Color Density) to change the appearance of the
gradient.
Note that because the coloring algorithm decides how the gradient is used, the resulting colors in the
layer may or may not be directly related to the colors in the gradient.
You can tell when a direct coloring algorithm is selected in the Inside or Outside tab because the text
"Direct coloring algorithm" is visible below the title.
An example of a direct coloring algorithm is Direct Orbit Traps.
Next: Standard coloring algorithms
See Also
Coloring algorithms
Working with coloring algorithms
173
Standard coloring algorithms
Ultra Fractal comes with a set of standard coloring algorithms. They are located in the file
Standard.ucl in the Formulas folder. It contains the following coloring algorithms:
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Basic
Binary Decomposition
Decomposition
Direct Orbit Traps
Distance Estimator
Emboss
Exponential Smoothing
Gaussian Integer
Generic Coloring (Gradient, Direct)
Gradient
Image
Lighting
None
Orbit Traps
Smooth (Mandelbrot)
Triangle Inequality Average
All standard coloring algorithms are also implemented as coloring classes in Standard.ulb. This
makes it possible to use them with Generic Coloring or in other formulas that accept coloring classes.
See About classes and Example 2 - Orbit trap classes for more information.
See Also
Standard fractal formulas
Standard transformations
Coloring algorithms
Public formulas
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Basic
The Basic coloring algorithm implements four simple and classic ways of
coloring the outside areas of a fractal. It is useful for reproducing
fractals created with older fractal software.
Basic is available as a coloring algorithm in Standard.ucl and as a
coloring class in Standard.ulb.
The Coloring Type parameter selects how the fractal should be colored:
The Iterations option colors a pixel according to the number of iterations that were necessary for
the fractal formula to bail out (to decide that it's an outside pixel). This is the oldest method used to
color fractals. It creates images with bands of solid colors. To smoothen the bands, use the Smooth
(Mandelbrot) coloring algorithm.
The Real, Imaginary, and Sum options use the last value of z in combination with the number of
iterations to color pixels. They create smooth, true-color images. Good results are usually obtained if
the bail-out parameter of the fractal formula is not set too high. Try 4, for example.
See Also
Binary Decomposition
Distance Estimator
Standard coloring algorithms
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Binary Decomposition
The Binary Decomposition coloring algorithm uses just two colors from
the gradient. It colors fractals according to the "angle" of the last value
of z from the fractal formula. This results in quite abstract and elegant
images.
The two colors used are at the beginning and at the middle of the
gradient.
There is one parameter that selects between two different flavors of the same algorithm. Each option
creates different patterns. The second option reproduces the coloring used for many fractals in the
classic Beauty of Fractals book.
It often works well to combine this coloring algorithm with other layers that contain more different
colors. Furthermore, low values (for example 4) for the bail-out parameter of the fractal formula
usually give the best results.
Binary Decomposition is available as a coloring algorithm in Standard.ucl and as a coloring class in
Standard.ulb.
See Also
Basic
Decomposition
Standard coloring algorithms
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Decomposition
The Decomposition coloring algorithm colors fractals according to the
"angle" of the last value of z from the fractal formula. The angle is
decomposed and distributed over the full range of the gradient.
This coloring algorithm tends to create circular bands all over the image
that contain all colors from the gradient. Low values (for example 4) for
the bail-out parameter of the fractal formula usually give the best
results.
With convergent fractal types, such as Newton or Nova, Decomposition usually does not create
smoothly colored images, but it can still be interesting.
Decomposition is available as a coloring algorithm in Standard.ucl and as a coloring class in
Standard.ulb.
See Also
Basic
Binary Decomposition
Standard coloring algorithms
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Direct Orbit Traps
The Direct Orbit Traps coloring algorithm is a direct coloring algorithm.
This means that it the resulting images are not limited to the colors in
the gradient. It usually creates softly shaded, pastel-like images.
Direct Orbit Traps is available as a coloring algorithm in Standard.ucl
and as a coloring class in Standard.ulb. As a coloring class, it uses
several class parameters instead of normal parameters to make it easier
to add new trap shapes and coloring options. See Example 2 - Orbit trap classes and Combining
fractals with images for more information. You need to combine the Direct Orbit Traps class with
Generic Coloring (Direct).
Direct Orbit Traps works by calculating a color for every iteration. These colors are merged together
to obtain the final color for each pixel. This is like using multiple layers within a single coloring
algorithm.
The colors are taken from the gradient and merged onto the background color. If you change the
gradient, the layer is recalculated with the new colors. It can sometimes be difficult to predict the
effect of changes to the gradient, because the gradient colors are merged with each other and with
the background color.
Most of the parameters are shared with Orbit Traps. There are some additional parameters that
specify how the colors from each iteration are merged:
Base Color
Specifies the background color. All other colors are merged on top of
the background, so the background color interacts with the colors
from the gradient. The background color can also be transparent.
Specifies the merge mode used to merge colors on top of the
background. All layer merge modes are supported here.
Trap Color Merge
Additional Alpha
Remember to adjust the background color so it will work well with the
selected merge mode. For example, use a dark background color with
Screen, and a light background color with Multiply.
If set to distance, the opacity of the color calculated for each
iteration is reduced according to the distance from the trap shape.
This can create very soft and smooth images. (In the class version of
Direct Orbit Traps, this parameter is grouped with Color Trap.)
Trap Merge Opacity
Sets the opacity (between 0 and 1) of the color calculated for each
iteration. The opacity of the gradient is also taken into account, just
like when merging layers.
Trap Merge Order
Sets the order in which traps are merged. The bottom-up option
merges later iterations on top of the existing iterations, while the topdown option merges later iteration underneath the existing iterations.
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Color Trap
(Class version only.) This selects the color trap class which is
responsible for converting z values to colors. Normally, Trap Shape
Wrapper is selected, which wraps a trap shape class, a trap coloring
class and a gradient class to do this. However, you could also select
another class, such as Image Trap from common.ulb which returns
colors from an imported image.
See Also
Orbit Traps
Standard coloring algorithms
Example 2 - Orbit trap classes
Combining fractals with images
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Distance Estimator
The Distance Estimator coloring algorithm estimates the distance
between a pixel and the boundary of the fractal (for example the
boundary of the Mandelbrot set). The pixel is colored accordingly.
This coloring algorithm is especially good at showing the thin connecting
lines and miniatures that exist everywhere in the Mandelbrot set. It
works correctly for divergent fractal formulas like Mandelbrot, Julia, and
Phoenix.
The Exponent parameter should be set to match the exponent or power of the fractal formula (this
is usually also a parameter). Higher values (like 128) for the bail-out parameter of the fractal
formula give the best results.
Distance Estimator is available as a coloring algorithm in Standard.ucl and as a coloring class in
Standard.ulb.
See Also
Basic
Decomposition
Standard coloring algorithms
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Emboss
The Emboss coloring algorithm interprets results from one of the
Embossed fractal formulas to create fractals with 3D contour lines. It is
unlikely to give good results with other fractal formulas.
See Embossed (Julia, Mandelbrot, Newton) for more information.
Emboss is available as a coloring algorithm in Standard.ucl and as a
coloring class in Standard.ulb.
See Also
Lighting
Standard coloring algorithms
181
Exponential Smoothing
The Exponential Smoothing coloring algorithm creates smoothly colored
outside areas. It works well for both convergent and divergent fractal
types, which means that it can be combined with almost any fractal
formula.
Fractal formulas like Mandelbrot, Julia, and Phoenix have only divergent
orbits, while types like Newton and Nova have only convergent orbits.
The Magnet fractal formulas have both divergent and convergent orbits.
With the Color Divergent and Color Convergent parameters, you can enable coloring for divergent
and convergent orbits. You should always enable at least one option. The formula runs slightly faster
if you just enable the necessary options (only Magnet-like fractals require both parameters to be
enabled).
The Divergent Density parameter can be used to tweak the color density for divergent parts of a
fractal. It is only useful when both divergent and convergent orbits exist in the fractal.
Exponential Smoothing is available as a coloring algorithm in Standard.ucl and as a coloring class in
Standard.ulb.
See Also
Smooth (Mandelbrot)
Standard coloring algorithms
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Gaussian Integer
The Gaussian Integer coloring algorithm colors fractals according to how
the calculated orbits are related to Gaussian integers.
Gaussian Integer is available as a coloring algorithm in Standard.ucl, or
as a trap shape class in Standard.ulb that can be used together with the
Orbit Traps or Direct Orbit Traps coloring classes. See Example 2 - Orbit
trap classes.
Gaussian integers are complex numbers normalized to integer values. This coloring algorithm
examines the values of z calculated by the fractal formula, and tests them against nearby Gaussian
integers.
The resulting images are richly textured, containing many circles, dots, and stars. By tweaking the
provided parameters, many variations are possible.
The following parameters are available:
Integer Type
Specifies the rounding method to use to find the nearest Gaussian
integer. The round(z) option usually gives smoother images than the
other options.
Color By
Selects how the color of each pixel is determined. For example, it can
be colored by the minimum distance from a value of z to the nearest
Gaussian integer.
Normalization
Chooses between several ways of normalizing the distance to the
nearest Gaussian integer. If you select factor or f(z), an additional
parameter will appear that specifies the normalization factor or
function to use.
If checked, a small randomization factor is added to each value of z
before examining its behavior. Additional parameters will appear to
specify the amount of randomization and a seed value. Each seed
value will give different randomization patterns.
Randomize
In the trap shape class version, this option is not available. However,
you can achieve the same effect by selecting the Randomize
transformation class from Standard.ulb for the Trap Position
parameter in the Orbit Traps class.
See Also
Example 2 - Orbit trap classes
Orbit Traps
Standard coloring algorithms
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Generic Coloring (Gradient, Direct)
Generic Coloring is a skeleton coloring algorithm that lets a coloring
class do the actual work. All coloring algorithms in Standard.ucl are also
implemented as coloring classes. You can select any of these as the
coloring class to be used together with Generic Coloring.
There are two versions of Generic Coloring: a gradient version and a
direct version. Generic Coloring (Gradient) is a normal coloring
algorithm and works only with gradient coloring classes which return an
index into the gradient.
Generic Coloring (Direct) is a direct coloring algorithm and works with coloring classes that directly
return a color. It also works with gradient coloring classes, but in that case changes to the gradient
trigger an unnecessary recalculation.
The Coloring Algorithm class parameter sets the coloring class to be used. By default, the Smooth
(Mandelbrot) class from Standard.ulb is selected for Generic Coloring (Gradient), while Generic
Coloring (Direct) defaults to the Direct Orbit Traps class.
An example of using Generic Coloring is given in Example 2 - Orbit trap classes.
See Also
About classes
Standard coloring algorithms
Standard classes
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Gradient
The Gradient coloring algorithm ignores the information from the fractal
formula and fills the fractal with all colors from the gradient.
To obtain a completely filled image, select the Gradient coloring
algorithm in both the Inside and the Outside tabs of the Layer Properties
tool window. This ensures that all pixels are colored in the same way.
The Gradient Type parameter selects how the gradient should be displayed: linear (from left to
right), radially, or as a cone. Use zooming and panning to reposition the gradient as desired.
This coloring algorithm is handy for creating special effects with multi-layer images. You can, for
example, use it in a mask together with a suitable transparent gradient to show only selected
portions in a regular pattern of the layer that is masked.
Gradient is available as a coloring algorithm in Standard.ucl and as a coloring class in Standard.ulb.
See Also
Standard coloring algorithms
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Image
The Image coloring algorithm enables you to load an external image into
a fractal. It simply displays the image in the inside or outside area of the
fractal. If you want the entire layer to show the image, the Image
coloring algorithm is best combined with the standard Pixel fractal
formula.
The Image parameter contains the image that is displayed. See Using
images for more information on how to use this parameter.
In the layer, the image is scaled such that it occupies the entire layer if the default location is set. To
achieve this, load the Pixel fractal formula and click the Reset Location button on the Location tab. Of
course, you can pan, zoom, and rotate at will to frame or distort the image.
When zooming in, the individual pixels in the image are interpolated using sophisticated bicubic
interpolation methods. For the best results when zooming out, it is recommended to render the
fractal with anti-aliasing enabled.
Image is available as a coloring algorithm in Standard.ucl and as a coloring class in Standard.ulb.
See Also
Standard coloring algorithms
Using images
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Lighting
The Lighting coloring algorithm interprets results from one of the Slope
fractal formulas to create fractals with 3D lighting effects. It will
probably not give very good results with other fractal formulas.
See Slope (Julia, Mandelbrot, Newton) for more information.
Lighting is available as a coloring algorithm in Standard.ucl and as a
coloring class in Standard.ulb.
See Also
Emboss
Standard coloring algorithms
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None
The None coloring algorithm is the simplest coloring algorithm available.
It is loaded by default in Ultra Fractal when a new fractal is created.
None reproduces the standard iterations coloring algorithm found in
most fractal software.
None is available as a coloring algorithm in Standard.ucl and as a
coloring class (called Default) in Standard.ulb.
See Also
Basic
Standard coloring algorithms
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Orbit Traps
The Orbit Traps coloring algorithm is an extremely versatile generalpurpose coloring algorithm. It can be applied to almost any fractal
formula with good results, on both the Inside and Outside tabs.
Orbit Traps is available as a coloring algorithm in Standard.ucl and as a
coloring class in Standard.ulb. As a coloring class, it uses several class
parameters instead of normal parameters to make it easier to add new
trap shapes and coloring options. You need to combine the Orbit Traps class with Generic Coloring
(Gradient). See Example 2 - Orbit trap classes for an example of how this works in practice.
Orbit Traps works by examining the value of z (as calculated by the fractal formula) for each
iteration. It tests how close z is to a fixed shape (the orbit trap), and colors the pixel according to the
closest distance, for example.
The possibilities are almost unlimited because there are so many combinations of parameters
available. It is a good idea to take some time to explore the different options in here.
The following parameters are available:
Trap Position
(Class version only.) Provides options to transform the value of z before it is
passed to the trap shape class. This essentially transforms the trap shape.
The default Trap Position class provides many common options, but it is also
possible to select any other transformation class, or even to merge multiple
transformations with Transform Merge in common.ulb.
Specifies the shape of the orbit trap. Some options may not look too exciting
with the default settings of the other parameters, but try changing Trap
Coloring and Trap Mode in that case. Not all options work equally well with
all fractal types.
Trap Shape
In the class version, Trap Shape is a class parameter that accepts any trap
shape class. All trap shapes from the Orbit Traps coloring algorithms are
available as trap shape classes in Standard.ulb.
Some trap shapes have additional parameters:
Diameter
Specifies the diameter or size of the trap. Larger values usually create
decorations further away from the center of the fractal.
Order
Specifies the order for the trap, such as the number of leaves for the pinch
trap shape. It depends on the trap shape how this is interpreted. Larger
values usually give more complex traps.
Frequency
Specifies the frequency of ripples or waves (where applicable). Larger values
create "busier" trap shapes with more frills.
Trap Transfer
(Class version only.) Provides options to transform the distance that is
returned by the trap shape class. The default Trap Transfer class is quite
powerful, but it is also possible to select another transfer class.
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Selects how the values gathered at each iteration are interpreted to produce
a color. For example, the magnitude at the closest distance to the trap
shape is used if Trap Coloring is set to magnitude, and Trap Mode to
closest.
Trap Mode
Experiment to see which combinations work well together. Some trap modes
only work well with specific trap coloring settings, for example.
The trap only option will show the trap shape only. This is useful for
learning how the other options work.
In the class version, Trap Mode is a class parameter that accepts any trap
mode class, and the original trap mode options are now also available as
trap mode classes in Standard.ulb.
Trap Threshold
Specifies the width of the trap area, used for most trap modes. (In the nonclass version, this parameter is called Threshold.)
The Trap Coloring parameter selects what information is gathered at each
iteration. This is later filtered and combined to produce the final color.
Trap Coloring
Use Solid Color
In the class version, Trap Coloring is a class parameter that accepts any trap
coloring class, and the original trap coloring options are now also available
as trap coloring classes in Standard.ulb.
If checked, areas outside the trap shape will be colored with the solid color
(allowing them to be transparent).
The non-class version of Orbit Traps does not have the Trap Position class parameter that allows any
transformation to transform the trap shape, but it does offer some transformation options:
Trap Center
Specifies the center of the trap shape. Values other than (0, 0) will distort
the trap shape into the direction of the trap center. Use the eyedropper to
select good values for this parameter.
Aspect Ratio
Changes the aspect ratio of the trap shape. Values larger than 1 will stretch
the trap horizontally; values smaller than 1 will stretch it vertically.
Rotation
Rotates the trap shape in clockwise direction (specified in degrees).
See Also
Tutorial: Masking
Example 2 - Orbit traps classes
Direct Orbit Traps
Standard coloring algorithms
190
Smooth (Mandelbrot)
The Smooth (Mandelbrot) coloring algorithm creates smoothly colored
outside regions with fractal formulas such as Mandelbrot and Julia.
It works with most divergent fractal formulas. For Newton and Nova
fractals, use Exponential Smoothing instead.
There are two parameters available: Exponent and Bail-out value.
These should be set to match the corresponding parameters of the fractal formula. Otherwise, the
coloring will not be perfectly smooth.
Usually, the best results are obtained when the Transfer Function in the Outside tab is set to Log.
Smooth (Mandelbrot) is available as a coloring algorithm in Standard.ucl and as a coloring class in
Standard.ulb.
See Also
Basic
Standard coloring algorithms
191
Triangle Inequality Average
The Triangle Inequality Average coloring algorithm creates smoothly
colored fractals with large flame-like patterns that extend from the
fractal outwards.
Because it uses the same smoothing as Smooth (Mandelbrot), it only
works with most divergent fractal formulas, such as Mandelbrot and
Julia.
There are two parameters available: Exponent and Bailout. These should be set to match the
corresponding parameters of the fractal formula. Otherwise, the coloring will not be smooth.
Use very large bail-out values for good results. The default value 1e20 (a 1 with 20 zeroes) is a good
starting point. The Mandelbrot (Built-in) formula cannot handle such large values, so use the nonbuilt-in Mandelbrot instead.
Triangle Inequality Average is available as a coloring algorithm in Standard.ucl and as a coloring
class in Standard.ulb.
See Also
Orbit Traps
Standard coloring algorithms
192
Transformations
Transformations globally transform and warp the shape of a fractal. You can combine various
transformations to create complex effects. Of course, you can also write your own transformations.
Transformations are managed in the Mapping tab of the Layer Properties tool window:
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The Add button opens a modal browser to select a new transformation. The transformation
is then added to the list.
The Delete button removes the selected transformations from the list.
The Reload button reloads the selected transformation from disk and recalculates the layer.
The Edit button opens the selected transformation in the formula editor.
The More button shows a menu with additional commands.
The Enable icon before a transformation quickly enables and disables the transformation.
The Solid Color swatch specifies the solid color for the selected transformations. The solid
color can be used by a transformation for special purposes. See Solid color.
The transformation parameters are additional parameters specific to the selected
transformations. See Formula parameters.
You can resize the transformations list by dragging the area just above the line that divides the Solid
Color setting from the transformation parameters. The Reload and Edit buttons hide themselves
automatically when there is not enough space. In this case, these commands can be found on the
More menu.
Next: Working with transformations
See Also
Tutorial: Learning about transformations
Standard transformations
193
Fractal formulas
Coloring algorithms
194
Working with transformations
You work with transformations in the Mapping tab of the Layer Properties tool window. The Mapping
tab shows a list with the transformations used by the active layer.
Transformations are stored in transformation files (*.uxf). Each file can contain multiple
transformations.
To add a transformation, click the Add button. This opens a modal browser that shows the
transformation files on your computer and the transformations that they contain. Doubleclick on a transformation to add it.
Hold down the Add button to open a menu with transformation presets. See Presets.
To remove the selected transformations, click the Delete button.
To rename the active transformation, click it again or press F2 (like in Windows Explorer).
To change the order in which transformations appear in the list, drag them up or down. See
Multiple transformations.
The Enable icon before each transformation enables and disables it. Use it to temporarily
disable a transformation so you can judge its effect, or adjust other transformations.
Some transformations contain additional help. To access it, click the More button, and then
click Help from the menu that opens. This menu also provided commands to copy and
paste the settings and parameters for the selected transformation, and to reset all
parameters to the default values.
The bottom pane of the Mapping tab contains parameters specific to the selected transformations.
These parameters work the same as the parameters for fractal formulas. See Formula parameters.
Notes
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You can select multiple transformations by holding down the Ctrl key while clicking a
transformation. Hold down the Shift key while clicking to select a range of transformations.
This enables you to easily edit multiple transformations together, like you can do with layers.
If multiple layers are selected, the list in the Mapping tab only shows those transformations
that all selected layers have in common.
Right-click inside the list of transformations to open a menu with frequently used commands.
Next: Multiple transformations
See Also
Tutorial: Learning about transformations
Transformations
Standard transformations
Public formulas
195
Multiple transformations
Ultra Fractal lets you combine multiple transformations to achieve more complex effects. With more
than one transformation, the order in which the transformations appear in the list in the Mapping tab
of the Layer Properties tool window is important.
You can view a transformation as if it transforms the image of the layer as produced by the fractal
formula and the coloring algorithms. (In fact, it works differently, but you can ignore that unless you
are writing your own transformations.)
The transformations are then processed from the bottom of the list to the top. So, if you have two
transformations, the top one works on the "image" produced by the second transformation.
Here is an example to illustrate this:
Original
Inverse
Lake
Two variations on the original image are shown. The first uses the Inverse transformation that turns
an image "inside out". The second variation uses the Lake transformation that mirrors the image
horizontally and creates the illusion of water ripples.
What happens if we combine the two transformations?
First Lake, then Inverse
First Inverse, then Lake
If we put Inverse above Lake, we get the first image. If we put Lake on top instead, the second
image is produced. This shows that a transformation works on the intermediate result produced by
the transformations below it.
Notes
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You can freely experiment with the order of the transformations by dragging them up or
down in the list.
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When you add a new transformation, it is always inserted above the selected transformation,
so it works on the intermediate image produced by that transformation.
Next: Solid color
See Also
Transformations
Working with transformations
197
Solid color
In the Mapping tab of the Layer Properties tool window, you can specify a solid color for each
transformation. A transformation can use this color for special purposes.
For example, a transformation that maps a fractal onto a plane in 3D space also needs to color the
area that is above or below the plane. This area is usually colored with the solid color.
This example shows a simple fractal mapped onto a sphere with the 3D Mapping transformation. The
area outside the sphere is given the solid color (in this case black).
To change the solid color, click on the Solid Color swatch in the Mapping tab. By default, it is set to
black, but you can choose any color. You can also change the opacity. By setting the opacity to 0,
the solid color and thus the solid areas will become transparent, so the lower layers will become
visible.
In effect, the transformation not only transforms the shape of the fractal, but also generates a mask
for the layer.
Some transformations are only intended to create masks, and do not transform the pixels at all. You
should use them with a transparent solid color. An example is the Clipping transformation.
Notes
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If you make a solid color transparent, layer transparency will be enabled automatically. See
Transparent layers.
The masks created with transformations always have sharp edges. For soft masking with
more control over the masking shapes, use layer masks instead. See Masks.
Next: Standard transformations
198
See Also
Transformations
Working with transformations
199
Standard transformations
Ultra Fractal comes with a set of standard transformations. They are located in the file Standard.uxf
in the Formulas folder. It contains the following transformations:
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3D Mapping
Aspect Ratio
Clipping
Generic Clipping
Generic Transformation
Glass Hemisphere
Inverse
Kaleidoscope
Lake
Mirror
Ripples
Twist
All standard transformations are also implemented as transformation or clip shape classes in
Standard.ulb. This makes it possible to use them with Generic Transformation or Generic Clipping, or
in other formulas that accept transformation classes. See About classes for more information.
See Also
Standard fractal formulas
Standard coloring algorithms
Standard classes
Transformations
Public formulas
200
3D Mapping
The 3D Mapping transformation maps a fractal onto a three-dimensional
shape, such as a plane or a sphere. It is available as a transformation in
Standard.uxf and as a transformation class in Standard.ulb.
Once this transformation is in effect, normal zooming and panning will
just move the 3D shape around with the fractal on it. If you want to
zoom into the fractal as it is mapped onto the shape, use the Fractal
Center, Fractal Magnification, and Fractal Rotation parameters.
To use the rotation and translation parameters effectively, you need to understand the left-handed
3D coordinate system used by the transformation. Here, the X-axis points to the left, the Y-axis
points upwards, and the Z-axis points into the screen. So, if you use a positive Z-translation, the 3D
shape will appear to move away, into the screen.
The following parameters are available:
Shape
Selects the type of 3D shape that the fractal is mapped onto. In the
class version of 3D Mapping, this is a class parameter that lets you
select any class that implements a mapping shape.
X Rotation
Y Rotation
Z Rotation
Rotates the 3D shape around the X, Y, or Z axis. To predict the
direction of rotation, hold up your left hand with your thumb
pointing into the positive axis direction (for example, to the left for
X rotation). Your (curled) fingers now show the direction of positive
rotation around that axis.
X Translation
Y Translation
Z Translation
Moves the shape around in 3D space. You always need some
positive Z translation to move the shape "into" the screen, otherwise
you will be "inside" the shape and it won't be visible. With the plane
shape, use a negative Y translation to look down upon it.
Fractal Center
Fractal Magnification
Fractal Rotation
Specifies the location of the fractal as it is mapped onto the shape.
When adding the transformation, the current coordinates will be
used (remember to reset the location to get a proper view of the 3D
shape).
The easiest way to specify a location is to copy the coordinates from
the Location tab of a different fractal window that contains the same
fractal formula without the 3D Mapping transformation.
See Also
Tutorial: Learning about transformations
Standard transformations
201
Aspect Ratio
The Aspect Ratio transformation can be used to create fractals for media
with non-square pixels. You should add it to all layers of the fractal. It is
available as a transformation in Standard.uxf and as a transformation
class in Standard.ulb.
The Aspect Ratio parameter specifies the aspect ratio (height / width)
of the final media. The final media is the computer screen or printed
poster that will eventually display the fractal. If the value of the parameter is equal to the height
divided by the width of the fractal window, no stretching occurs.
For example, suppose you would like to display a fractal on a 15" x 10" screen that has a resolution
of 400 x 300 pixels. Here, the pixels are wider than tall. You would set the width and height of the
fractal window to 400 x 300 to obtain the desired size. Then, set the Aspect Ratio parameter of this
transformation to 0.6667 (10" / 15").
Most computer monitors and printers have square pixels. In this case, you do not need to use this
transformation. If you just want to stretch the fractal, use the Stretch parameter in the Location tab
of the Layer Properties tool window instead.
See Also
Standard transformations
202
Clipping
The Clipping transformation cuts a geometric shape out of a fractal. The
shape is filled with a solid color. It can also be transparent, to make
parts of the underlying layers visible.
Clipping is available as a transformation in Standard.uxf and as a clip
shape class in Standard.ulb. In class form, it can be used together with
Generic Clipping. In this case, it also shows handles in the fractal
window to show where the edges of the clipping shape are.
Both rectangular and circular shapes are available. You can choose to cut either the region inside or
outside the shape. This makes the Clipping transformation also useful for creating frames.
The following parameters are available:
Center
Specifies the coordinates of the center of the clipping shape. Use the
eyedropper (right-click and click Eyedropper) to select the center by
clicking inside the fractal window.
Right Edge
Specifies the coordinates of the right edge of the clipping shape. Use the
eyedropper to select this.
Top Edge
Specifies the coordinates of the top edge of the clipping shape. Use the
eyedropper to select this.
Shape
Selects the type of shape to use. If you select circle or square, the Top
Edge parameter is ignored.
Allow Rotation
If checked, the shape is allowed to rotate. In this case, the Right Edge
parameter also defines the rotation to use.
Region
Selects whether to cut the region outside the clipping shape, or inside the
clipping shape. (This parameter is not available in the Clipping class.)
Screen-Relative
If checked, all coordinates are interpreted as relative to the screen. This
makes it harder to enter coordinates (because you can no longer use the
eyedropper), but it preserves the location of the clipping shape relative to
the screen when zooming. (This parameter is not available in the Clipping
class.)
See Also
Tutorial: Learning about transformations
Standard transformations
203
Generic Clipping
The Generic Clipping transformation cuts a shape out of a fractal. The
shape is determined by a clip shape class, and Generic Clipping allows
any compatible clip shape class to be selected.
By default, the Clipping class from Standard.ulb is selected.
The following parameters are available:
Clipping Region
Screen-Relative
Coordinates
Clipping Shape
Selects whether to cut the region outside the clipping shape, or inside the
clipping shape.
If checked, all coordinates are interpreted as relative to the screen. This
makes it harder to enter coordinates (because you can no longer use the
eyedropper), but it preserves the location of the clipping shape relative to
the screen when zooming. The coordinates are interpreted with (0, 0) at
the lower left corner of the fractal window and (1, 1) at the upper right
corner.
This is the clip shape class parameter. You can select any class that
represents a clipping shape.
Generic Clipping can also show handles around the edges of a clipping shape. The number and
position of these handles are determined by the selected clipping shape. By default, handles are
shown in the fractal window, but not when rendering or on previews. Under Handle options, this
can be configured:
Show Handles
Sets whether handles are displayed at all.
Not on previews
If checked, handles are hidden on previews, for example in the browser or
for explore or eyedropper previews.
Not on renders
If checked, handles are hidden when rendering to disk.
Show Numbers
If checked, a number or label is displayed next to each handle if
applicable.
Show Lines
If checked, lines are displayed if applicable.
Handle Size
Adjusts the apparent size of the handles.
Handle Thickness
Adjusts the apparent thickness of the handles.
Note: Handles are shown by toggling the solid color of the transformation on and off, so you might
not see them properly if the solid color does not contrast with the fractal. Also, they do not work well
in combination with the Guessing drawing method.
See Also
About classes
Standard transformations
Standard classes
204
Generic Transformation
Generic Transformation is a skeleton transformation that lets a
transformation class do the actual work. All transformations in
Standard.uxf are also implemented as transformation classes. You can
select any of these as the transformation class to be used together with
Generic Transformation.
The Transformation class parameter sets the transformation class to
be used. By default, the Inverse class from Standard.ulb is selected.
See Also
About classes
Standard transformations
Standard classes
205
Glass Hemisphere
The Glass Hemisphere transformation displays the fractal as though it is
viewed through a spherical lens. It is available as a transformation in
Standard.uxf and as a transformation class in Standard.ulb.
The location, size, and apparent refractive index of the lens can be
changed. The refractive index adjusts the strength of the lens.
The following parameters are available:
Refractive index
Width
Specifies the refractive index of the lens. You can use this to simulate
various glass-like materials. Larger values will increase the strength of
the lens.
Specifies the width of the lens in fractal coordinates.
Center
Specifies the coordinates of the center of the lens. Use the eyedropper
(right-click and click Eyedropper) to select the center by clicking inside
the fractal window.
Use Screen Center
If checked, the center of the screen is used instead of the Center
parameter, so the lens is always centered on the screen, even when
zooming in.
See Also
Standard transformations
206
Inverse
The Inverse transformation turns a fractal inside out. The original center
of the fractal is put infinitely far away, and points that were far away
end up near the center. Inverse is available as a transformation in
Standard.uxf and as a transformation class in Standard.ulb.
This can change the shape of the fractal in unexpected ways. The
example image shows the Inverse transformation applied to a standard
Mandelbrot set. (The inside areas of the Mandelbrot set are colored
gray.)
The following parameters are available:
Radius
Center
Use Screen Center
Specifies the radius of the inversion circle. The transformation inverts all
points around this circle. Larger values will simply magnify the inverted
fractal.
Specifies the coordinates of the center of the inversion circle. This will
drastically change the shape and form of the fractal. Use the eyedropper
(right-click and click Eyedropper) to select the center by clicking inside
the fractal window.
If checked, the center of the screen is used instead of the Center
parameter, so the inversion circle is always centered on the screen. This
can give unexpected effects when zooming in.
See Also
Standard transformations
207
Kaleidoscope
The Kaleidoscope transformation fills the screen with rotated copies of a
small radial slice of the fractal, creating a kaleidoscope effect. It is
available as a transformation in Standard.uxf and as a transformation
class in Standard.ulb.
By tweaking the parameters, you can simulate many different kinds of
symmetry. By default, the slices are aligned and mirrored to make the
edges match, but there are also other options that produce sharp transitions.
Try experimenting with the Center and Rotation angle parameters to obtain good results. Some
sections of the fractal lend themselves much better to the kaleidoscope effect than others.
The following parameters are available:
Symmetry Order
Symmetry Mode
Sets the symmetry order. This is the number of times the slice of the
fractal is copied and rotated to obtain the final image.
Selects the symmetry mode to use. Only the reflective option is
guaranteed to produce seamless images. Use the slice only option to
view the slice of the fractal that is used as a base for the symmetry
effect.
Specifies the coordinates of the symmetry center. Together with the
Rotation angle parameter, this selects the slice of the fractal that is
used. Try changing this to see the various effects that are possible.
Center
Use the eyedropper (right-click and click Eyedropper) to select the
center by clicking inside the fractal window.
Use Screen Center
If checked, the center of the screen is used instead of the Center
parameter, so the symmetry center is always centered on the screen.
This can give unexpected effects when zooming in.
Rotation angle
Rotates the fractal before determining the slice that will be used as a
base for the symmetry effect. This can drastically change the resulting
image.
See Also
Mirror
Standard transformations
208
Lake
The Lake transformation mirrors the fractal in a rippled lake. The top
part of the fractal is not altered, but below the water level, everything is
mirrored. It is available as a transformation in Standard.uxf and as a
transformation class in Standard.ulb.
By changing the parameters, you can adjust the height and rotation of
the water level, and change the size and frequency of the waves.
The following parameters are available:
Water level
Selects the water level. Only the imaginary part of this parameter
is used. Use the eyedropper (right-click and click Eyedropper) to
select the water level by clicking on a point inside the fractal
window.
Use screen center
If checked, the water level is always centered on the screen. In
this case, the Water level parameter is ignored.
Rotation angle
Rotates the water level. To rotate the fractal instead of the water,
also enter the same value in the Rotation angle parameter on the
Location tab.
Use Location tab angle
If checked, the rotation angle from the Location tab is used
instead of the Rotation angle parameter. This ensures that the
water level is always horizontal.
Amplitude
Frequency
Specifies the amplitude of the waves.
Specifies the frequency of the waves.
See Also
Ripples
Standard transformations
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Mirror
The Mirror transformation mirrors the fractal along an arbitrary axis. It
can be useful for mirroring effects with multiple layers. It is available as
a transformation in Standard.uxf and as a transformation class in
Standard.ulb.
There are presets for a horizontal and a vertical reflection axis, but you
can also specify any angle. The center of the axis is configurable, too.
The following parameters are available:
Reflection Axis
Reflection Angle
Selects the reflection axis. The axis points into the mirroring direction,
so it is perpendicular to the imaginary mirror. Select arbitrary to
specify any angle for the axis.
Specifies the rotation angle of the reflection axis, in degrees.
Center
Selects the center of the reflection axis. Use the eyedropper (rightclick and click Eyedropper) to select a point by inside the fractal
window.
Use screen center
If checked, the reflection center is always centered on the screen. In
this case, the Center parameter is ignored.
See Also
Kaleidoscope
Standard transformations
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Ripples
The Ripples transformation adds a water ripple effect to the fractal. The
center, strength, and frequency of the ripples are adjustable. It is
available as a transformation in Standard.uxf and as a transformation
class in Standard.ulb.
Interesting interference effects are obtained by adding multiple Ripple
transformations to a fractal, with different center and strength values.
The following parameters are available:
Ripple Center
Specifies the center of ripples. Use the eyedropper (right-click and
click Eyedropper) to select this by clicking on a point inside the fractal
window.
Use Screen Center
If checked, the ripple center is always centered on the screen. In this
case, the Ripple Center parameter is ignored.
Ripple Strength
Specifies the strength of the ripples. Larger values give a larger
distortion.
Ripple Frequency
Specifies the frequency of the ripples. Larger values will create more
and smaller ripples.
Ripple Fade
Specifies how soon the ripples fade out. Larger values cause the
ripples to fade out over a larger distance (so more ripples are visible).
Ripple Type
Selects how the ripples distort the fractal. The default Forward and
Back option gives the most natural water-like effect, but the other
options are also interesting.
See Also
Lake
Twist
Standard transformations
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Twist
The Twist transformation adds a twisted spiral to the fractal. It distorts a
small part of the fractal in the form of a spiral, like a vortex. It is
available as a transformation in Standard.uxf and as a transformation
class in Standard.ulb.
The center, strength, and size of the vortex are adjustable. This
transformation is often combined with the Ripples transformation to
obtain interference effects.
The following parameters are available:
Twist Center
Specifies the center of the twisted spiral. Use the eyedropper (rightclick and click Eyedropper) to select this by clicking on a point inside
the fractal window.
Strength
Specifies the strength of the twist. Larger values create more strongly
twisted spirals.
Decay Factor
Specifies how soon the spiral loses its strength. Larger values
decrease the size of the spiral.
See Also
Lake
Standard transformations
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About classes
Since the first release of Ultra Fractal in 1998, the formulas written for it
have become larger and more complex. Even though many formulas are
quite similar, they could not share any common code, but had to be
written as stand-alone formulas. For example, if you wanted to add just
one new feature to an existing formula written by someone else, you
had to create a new formula, duplicate all the code from the original
formula, and only then add some new things.
To improve this situation, formulas in Ultra Fractal 5 can re-use common code via classes. You can
view a class as a "black box" that adds functionality to a formula. Via class parameters, a formula
enables you to select the actual class that performs an action for the formula.
The formula declares what kind of functionality it needs and you can select any compatible class to
actually implement it. This makes it possible for formula authors to write a new class to implement
just the new feature that they want to add to an existing formula. The formula doesn't have to be
changed at all. You just select the new class when you use the formula.
For formula authors, classes make it easier to write and manage complex formulas. For everyday
users, classes make it possible to combine existing elements in new ways without needing to do any
programming.
Next: Example 1 - Formula classes
See Also
Fractal formulas
Writing formulas
213
Example 1 - Formula classes
Tip: This example assumes that you are familiar with Ultra Fractal basics as explained in the
tutorials.
As a first example of how classes work in practice, let's take a look at some of the standard classes
that come with Ultra Fractal.
First, use the browser to open the Default parameter set in Examples.upr.
Click the Browse button in the Formula tab of the Layer Properties tool window to select
Generic Formula in Standard.ufm.
Generic Formula is a "skeleton" formula that lets a class implement the actual fractal formula
behavior. It has just one class parameter called Fractal Formula which is set to the Mandelbrot class
by default:
The Mandelbrot class has its own parameters like Starting point, which appear grouped with the class
parameter. Let's select a different formula class.
Click the Browse button for the Fractal Formula class parameter to select a new class. This
opens the browser in class mode, so it shows only those classes that are compatible with
this class parameter.
Locate the Newton class in Standard.ulb and click OK.
Now, a Newton fractal appears instead of a Mandelbrot fractal. Anyone could write a formula class
that works with Generic Formula to create a different fractal, without having to modify Generic
Formula itself. Of course, this doesn't really do anything new, since you could also just write a new
fractal formula. But it does make the formula behavior available in a generic form.
Click the Browse button for the Fractal Formula class parameter again, and this time,
select the Slope class.
Briefly go to the Outside tab of the Layer Properties and click the Browse button there to
select the Lighting coloring algorithm. Then go back to the Formula tab again.
The combination of the Slope formula class and the Lighting coloring algorithm creates a 3D lighting
effect. Previously, there were three different Slope formulas for Mandelbrot, Julia, and Newton
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fractals (these are still in Standard.ufm). Each of these formulas duplicates the code for the lighting
effect; the only different code is the where the actual fractal formula calculation is done. Adding a
new fractal type could only be done by creating yet another variation of this formula.
However, now the Slope formula class contains another class parameter that enables you to select
the internal fractal formula. You can select any formula class, just like with Generic Formula.
Click the Browse button for the Fractal Formula class parameter inside the Slope class
(which currently is set to Mandelbrot) and select Phoenix (Mandelbrot) instead.
Suddenly, we have a Slope formula that works with any fractal type. New fractal types can be added
simply by writing them as a formula class, which makes them available for Generic Formula, Slope,
or any other place where a fractal formula can be inserted.
Next: Example 2 - Orbit trap classes
See Also
About classes
Fractal formulas
Writing formulas
215
Example 2 - Orbit trap classes
Tip: This example assumes that you are familiar with Ultra Fractal basics as explained in the
tutorials.
In the previous example, we saw how a class can implement the behavior of an entire fractal
formula. However, it's also possible to use classes in a more fine-grained way, exposing all aspects
of a formula for maximum flexibility.
The Orbit Traps coloring class is an example of this. The old Orbit Traps coloring algorithm (still
available in Standard.ucl) contained parameters such as trap shape, trap mode and trap coloring,
each with a number of options. In the new version, implemented as a coloring class in Standard.ulb,
these are now class parameters. Every option is now a separate class. Let's have a look:
First, use the browser to open the Default parameter set in Examples.upr.
Click the Browse button in the Outside tab of the Layer Properties tool window to select
Generic Coloring (Gradient) in Standard.ucl.
Like Generic Formula, Generic Coloring (Gradient) is a skeleton coloring algorithm that lets a coloring
class do the work. By default, it loads with the Smooth algorithm.
Click the Browse button for the Coloring Algorithm parameter to select the Orbit Traps
class in Standard.ulb.
As you can see, the Orbit Traps class uses class parameters for all major parameters. All trap
shapes, for example, are now implemented as separate classes. Let's select a different trap shape.
Click the Browse button for the Trap Shape parameter to select the Gaussian Integer
class.
The old Gaussian Integer coloring algorithm in Standard.ucl actually is a variation on an orbit trap,
just with a different trap shape. It had limited options to color the trap shape, but now that it is
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available as a general trap shape class, we can combine it with any trap mode or trap coloring.
For example, you can select Angle to Origin 2 as the trap coloring to get an effect that you couldn't
create with the original Gaussian Integer coloring algorithm.
When formula authors write new trap shapes, trap modes or trap colorings and make them available
in class library files via the public formula library, you can just drop them into this standard Orbit
Traps class to use them.
Next: Working with classes
See Also
About classes
Coloring algorithms
Writing formulas
217
Working with classes
Classes are commonly stored in class library files with an .ulb extension. Like all formula files, you
can examine and organize class library files with the browser. Make sure all files are visible, or set
the file type to Classes.
Usually though, you'll work with classes via class parameters.
Click the Browse button for a class parameter to select a different class. A modal browser
window opens, which shows only those classes that are compatible with this class
parameter.
Tip: In the browser window, click the Find Entries button and leave all fields blank to get a
list of all compatible classes in the formula library.
Hold down the Browse button for a menu with other options:
Click Copy to copy the currently selected class with all its sub-parameters to the Clipboard.
Click Paste to copy the class information on the Clipboard to the class parameter. The class
parameter must be compatible with the class parameter that you copied the class
information from, otherwise an error message is shown.
Click Reset Class to reset the class to the default class for the class parameter.
Click Reset Parameters to reset the sub-parameters for the currently selected class to
their default values. The class itself stays the same.
Click Edit to open the class declaration in the formula editor.
Next: Standard classes
See Also
About classes
Working with formulas
Writing formulas
218
Standard classes
All standard transformations, fractal formulas and coloring algorithms that come with Ultra Fractal
are also available as classes in the Standard.ulb file. This file is installed with the other standard
formula files in the main formula folder. For more information, see the documentation for the
standard formulas:
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Standard transformations
Standard fractal formulas
Standard coloring algorithms
For tips on how to use the standard classes, see the class usage examples.
Generally, to get as much formulas and classes working together as possible, it is necessary for them
to share the definition for common types of classes. These shared definitions are in the file
common.ulb. By adhering to these definitions, different formulas and classes from different formula
authors can easily work with each other. The common.ulb file is installed in the folder for public
formulas so it can be updated automatically via the online formula database when necessary.
The common.ulb file is intended mainly for formula authors. For everyday users, it does contain
some useful classes:
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Clip Shape Merge allows a single clip shape parameter to accept multiple clip shapes. See
Generic Clipping.
Image Trap allows an image to be used as a color trap for the Direct Orbit Traps coloring
class.
Transform Merge allows a single transformation parameter to accept multiple
transformations. See Generic Transformation.
Trap Shape Block and Trap Shape Merge allows a single trap shape parameter to accept
multiple trap shapes, and to transform trap shapes. See also Example 2 - Orbit trap classes.
For formula authors, the common.ulb file is invaluable and almost any class should be based on one
of the base classes found here. If you think modifications or new base classes are needed, please
contact [email protected] with your suggestion.
See Also
About classes
Writing formulas
219
Layers
One of Ultra Fractal's key features is the ability to use multiple layers. Each layer contains a separate
fractal image. By using multiple layers, you can achieve many special and wonderful effects that are
not possible with single-layer images.
Layers are managed in the Layers tab of the Fractal Properties tool window:
The layers list shows all layers of the active fractal window, complete with previews. It also selects
the active layer. The active layer is edited by the Layer Properties tool window and the gradient
editor.
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The Add button duplicates the active layer or group. Hold down the Add button to open a
menu with more options and layer presets. See Presets.
The New Group button adds a new layer group to the layers list. See Layer groups.
The Delete button deletes the currently selected layers.
The Merge Mode input box selects the merge mode of the selected layers.
The Opacity slider changes the opacity of the selected layers.
The Visible, Editable and Transparent icons before each layer toggle the visibility,
editability, and transparency of the layer. See Working with layers.
The Use as Mask button turns a layer into a mask and back. The Show Mask Only button
makes it easier to edit a mask. See Masks.
Next: How layers are merged
See Also
Tutorial: Working with layers
Keyboard shortcuts for the Fractal Properties tool window
Layer groups
220
Animating layers
221
How layers are merged
Within a multi-layered fractal, Ultra Fractal merges the different layers to create the resulting image.
This image appears in the fractal window. The layers are merged by superimposing them.
Ultra Fractal starts with the bottom layer and places the second layer on top of it. The third layer (if
any) is in turn placed on top of the result, and so on. If a layer is completely opaque, the layers
below it will be hidden. If a layer is completely transparent, it will not be visible.
Most layers will be more or less transparent, so they are visible while still allowing the lower layers to
shine through. There are four ways to make layers transparent:
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Reduce the opacity of the layer. By default, the opacity is set to 100%, making the layer
fully opaque. Move the opacity slider to the left to make the active layer more transparent.
Change the merge mode of the layer. By default, the merge mode is set to Normal. The
other merge modes create special effects that allow lower layers to be partially visible even if
the opacity of the layer is set to 100%. See Merge modes.
Make only parts of the layer transparent. The previous two options affect the entire layer.
You can, however, also change the opacity of only certain areas in the layer. See
Transparent layers.
Add a mask to the layer. The mask allows even more control over which areas of the layer
will be transparent. See Masks.
Of course, you can freely mix these options. It is common, for example, to use a merge mode like
Hard Light and set the opacity to less than 100%.
Next: Working with layers
See Also
Layers
Tutorial: Working with layers
222
Working with layers
Layers are managed in the Layers tab of the Fractal Properties tool window.
Click the Add button to add a new layer, duplicating the active layer.
Hold down the Add button to open a menu with layer presets. See Presets.
Click the Delete button to delete the currently selected layers.
Click the New Group button to create a new layer group. See Layer groups.
Most commands and tool windows (such as the Layer Properties tool window) work on the currently
selected layers. So, by selecting layers in the layers list, you change what is being edited by these
other tool windows.
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To select a layer, simply click it in the layers list.
To select multiple layers, hold down the Ctrl key and click the layers you want to add to
the selection. Ctrl-click a selected layer to deselect it again.
To select a range of layers, click the first layer. Then, hold down the Shift key and click the
last layer.
The Merge mode drop-down box selects the merge mode of the selected layers. The merge
mode determines how the layer is combined with the layers below it.
The Opacity slider adjusts the opacity of the selected layers. Move it to the left to make the
layer less visible (more transparent). Move it to the right to make it more opaque.
To rename the active layer, click it again or press F2 (like in Windows Explorer).
To move layers around in the list, drag the selected layers up or down. Of course, this
affects the way the layers are composited.
To the left of each layer is a row of icons. These icons toggle various properties.
The Visible icon toggles the visibility of the layer. Use it to temporarily hide a layer, so you
can more clearly see the other layers.
The Editable icon selects whether a layer is editable. Only editable layers are affected by
zooming operations. By default, all layers are editable, so if you want to zoom in on only one
layer, you should clear this icon on the other layers first.
The Transparent icon selects whether transparent areas in a layer are visible. See
Transparent layers.
Notes
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By holding down the Shift key while clicking on the Visible, Editable, or Transparent
icons, you toggle all other layers instead. If you want to see just one layer, for example,
Shift-click its Visible icon and all other layers will be turned off. Shift-click it again to show
all layers.
If a layer is not editable, its properties can still be changed with the Layer Properties tool
window. The Editable icon only affects zooming operations.
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To copy the selected layers to another fractal window, drag them from the list of layers to
the other fractal window.
Right-click in the list of layers to open a menu with frequently used commands. This menu
also contains Copy and Paste commands that are another way of copying layers to other
fractal windows.
Next: Merge modes
See Also
Tutorial: Working with layers
Working with masks
Keyboard shortcuts for the Fractal Properties tool window
Animating layers
224
Merge modes
The Merge mode drop-down box at the top of the Layers tab of the Fractal Properties tool window
selects the merge mode of the selected layers. The merge mode defines how a layer is combined
with the underlying layers to create the final image. The table below lists all merge modes and what
they do.
The best way to learn how to use the different merge modes is to experiment. Also try to use various
settings of the Opacity slider and see how it controls the intensity of the merging effects.
Next: Transparent layers
Merge mode
Description
Pass Through
This mode is only available for layer groups. The layers in the group will be
merged as if they were outside the group.
Normal
Directly returns colors from the layer. Use this if you don't want any special
effects.
Multiply
Multiplies the layer with the underlying layers. The result is always a darker
color, thus darkening the underlying layers.
Screen
Multiplies the inverse of the layer with the inverse of the underlying layers,
and inverts that again. The result is always a lighter color, thus brightening
the underlying layers. Screen is the inverse of Multiply.
Overlay
Multiplies or screens the colors, depending on the color in the underlying
layers. Creates color blending effects between the layer and the underlying
layers.
Hard Light
Multiplies or screens the colors, depending on the color in the layer.
Emphasizes the dark and light regions in the layer, while the areas with
medium brightness become transparent. Useful if the layer contains shadows
or embossing effects.
Soft Light
Darkens or lightens the colors, depending on the color in the layer. Creates an
effect similar to Hard Light, but with less emphasis on the dark and light areas
in the layer.
Darken
Returns the darkest of the color in the layer and the color in the underlying
layers.
Lighten
Returns the lightest of the color in the layer and the color in the underlying
layers.
Difference
Returns the difference between the layer and the underlying layers. Often
creates unusual and unexpected color transitions.
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Hue
Returns the hue of the layer, and the saturation and luminance of the
underlying layers. Colors the underlying layers with the hue of the layer.
Saturation
Returns the saturation of the layer, and the hue and luminance of the
underlying layers. Changes the saturation of the underlying layers depending
on the layer.
Color
Returns the hue and saturation of the layer, and the luminance of the
underlying layers. Colors the underlying layers with the layer. The underlying
layers control the brightness of the resulting image.
Luminance
Returns the luminance of the layer, and the hue and saturation of the
underlying layers. The layer controls the brightness of the underlying layers.
Luminance is the inverse of Color.
Addition
Directly adds the layer to the underlying layers, limiting the resulting colors at
white (255, 255, 255).
Subtraction
Directly subtracts the layer from the underlying layers, limiting the resulting
colors at black (0, 0, 0). Difference is similar, but returns the absolute value
after subtracting.
HSL Addition
Adds the layer to the underlying layers using the HSL color model. Creates
unusual effects.
Red
Returns the red part of the layer, and the green and blue parts of the
underlying layers.
Green
Returns the green part of the layer, and the red and blue parts of the
underlying layers.
Blue
Returns the blue part of the layer, and the red and green parts of the
underlying layers.
See Also
How layers are merged
Layers
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Transparent layers
To make a layer transparent, you can use the Opacity and Merge mode settings, but these work on
the entire layer. You can also make only certain parts of a layer transparent, which gives you more
artistic control.
The easiest way to create transparent areas in a layer is to use a transparent gradient. The
transparent parts of the gradient will create transparent areas in the layer. If you make all the other
layers invisible, a pattern of blocks will show the transparent areas.
Another way of creating transparent areas is to use the Solid Color setting of transformations and
coloring algorithms. Solid colors with an opacity value of less than 255 create transparent areas.
Many transformations, such as Clipping in Standard.uxf, use this to create masking effects.
The Transparent icon before the layer toggles transparent areas on and off. Use it to
quickly verify the transparent areas and to see what difference they make to the final image.
By default, transparency is off, but it is automatically turned on when you make changes to
transparent areas in the layer.
Next: Masks
See Also
Tutorial: Working with layers
How layers are merged
Layers
227
Masks
If you create transparent areas in a layer using a transparent gradient, the shape of the transparent
areas is controlled by the selected coloring algorithms. Certain colors in the gradient are transparent,
so those colors will become transparent in the layer, too. This means that you cannot use this method
to create arbitrarily shaped transparent areas.
If you use transformations instead and set the opacity of the solid color to less than 255, you can
create arbitrarily shaped transparent areas in the layer. You do need a transformation that will output
the area you need, but you could write it yourself. Still, a limitation of this technique is that pixels are
either set to the solid color (transparent), or they are colored according to the gradient and the
selected coloring algorithms. You can only create sharp edges, not smooth transitions.
Masks overcome these problems. A mask is an invisible layer that is attached to the layer that needs
transparent areas. The mask contains transparent areas, that are created with an ordinary
transparent gradient. Since the mask is invisible, these transparent areas are invisible as well.
Instead, the layer owning the mask "borrows" the transparent areas of the mask. The shape of these
areas is defined by the selected fractal formula, the selected coloring algorithms, and the gradient of
the mask. The shape is independent from the layer owning the mask.
Layer that needs transparent
areas
Mask with transparent areas
Layer with the mask applied
As you can see, the layer uses the transparent areas of the mask. The colors in the mask layer are
ignored.
Layers can have multiple masks to add differently shaped transparent areas. If the layer contains
transparent areas itself (for example created with a transparent gradient), these are also taken into
account.
Next: Working with masks
See Also
Tutorial: Masking
Layers
228
Working with masks
Masks are managed in the Layers tab of the Fractal Properties tool window.
To duplicate the active layer as a mask, hold down the Add button and click Duplicate as
Mask in the menu that appears.
To delete a mask, select it and click the Delete button.
To turn an existing layer into a mask, click the Use as Mask button. The layer will become a
mask, attached to the layer directly above it.
Click the Show Mask Only button to disable the layer owning the mask. Instead, the
transparent areas in the mask will be shown. White areas are opaque, black areas are
transparent. This makes it easier to edit the mask.
Usually, the mask will be entirely white because its gradient is not yet transparent. The first thing to
do is to open the gradient editor. Note that only the opacity view of the editor is enabled, since the
colors in the gradient do not matter for a mask. Add a few extra control points to the gradient so it
will start to show some transparency (darker regions).
By toggling the Show Mask Only button, you can alternatively work on the mask and judge the
effects that it has on the layer that owns it. The mask can be edited like any layer. For example, you
can zoom in on it, select another coloring algorithm, and so on.
Notes
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You can duplicate a mask layer like any other layer by clicking the Add button.
Layer groups can also have a mask. Just drag an existing mask layer onto the layer group,
or position the layer to use as a mask just below the group (but not in it) and click the Use
as Mask button.
Masks can be moved to other layers or layer groups simply by dragging them onto the
desired layer or layer group.
A layer or layer group can have more than one mask. In this case, the transparent areas in
the masks are combined, so each additional mask makes the layer more transparent.
Next: Layer groups
See Also
Tutorial: Masking
Masks
Working with layers
Layers
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Layer groups
You can organize the layers in a fractal with layer groups. A layer group can contain any number of
layers and nested layer groups. By logically arranging your layers in groups, the layers list becomes
easier to manage. In addition, you can apply masks and merge modes to the entire group, which
makes new creative effects possible.
Layer groups appear in the layers list with a folder-like group icon and a triangular
collapse/expand button. Click this button to hide or show the items in the group. Layers in a group
appear below it, indented to show their relationship.
Click the New Group button to create a new layer group. The layer group starts empty. To
fill the group, simply drag one or more layer onto the group to move them inside.
(Remember that you can Ctrl-click or Shift-click to select multiple layers.)
To delete a layer group, select it and click the Delete button. This also deletes all items that
the layer group contains. Tip: you can always undo unwanted deletions.
You can easily move layers in and out of groups by dragging them around. While you are dragging, a
thick black line shows where the dragged layers will end up. You can also nest groups simply by
dragging one group inside another. Another way to move layers in and out of groups is with the
Move Up and Move Down commands in the right-click menu for the layers list.
Layer groups have a merge mode just like layers, but with an additional Pass Through mode which
is the default. If Pass Through is selected, the layers in the group are merged with the underlying
layers one by one, as if they were not in a group at all. With the Pass Through merge mode and
Opacity at 100%, the layer group organizes its layers without introducing any visual changes.
If a merge mode other than Pass Through is selected, the layers in the group are first merged
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together. Then, that intermediate result is in turn merged onto the underlying layers with the merge
mode for the layer group. The resulting effect is often not possible to create without layer groups.
A group can also have a mask. In this case, the mask is applied to all layers in the group. Such a
mask appears below all other items in the group, aligned with the group itself, as shown in the
screen shot above. To turn a layer into a group mask, position it just under the group (but not inside
it), and click the Use as Mask button. To apply an existing mask to a group, simply drag it onto the
group. See also Working with masks.
See Also
Layers
How layers are merged
Masks
231
Animation
Note: You need Ultra Fractal Animation Edition to work with animations.
Any fractal in Ultra Fractal can easily be turned into an animation. You can animate all parameters of the
fractal at will and see the result immediately in the fractal window. Finally, render the animation to
watch it as a movie clip.
Creating and editing animations is done with various tools:
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The animation bar contains the time slider and vital animation controls that enable you to
create, edit, and play back animations. See Animation bar.
With the time slider, you set the current frame. The fractal window always displays the image
for the current frame.
The red animation indicators are shown if the fractal is currently in Animate mode. In Animate
mode, changes that you make to the fractal are only applied to the current frame. If Animate
mode is off (the default), your changes are applied to the entire range of frames.
The key icons show at which frames and for which parameters keys have been recorded. See
Animation keys.
The Timeline tool window provides an in-depth view of all animated settings and parameters
and can be used to edit and tweak your animations. See Timeline.
The following topics will explain how these tools work, and how to use them effectively.
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Next: Creating animations
See Also
Tutorial: Working with animations
233
Creating animations
Creating an animation from a normal fractal is easy, but perhaps different than in other fractal
programs. These steps show how to create a simple zoom movie.
Click New on the File menu, and then click Fractal to open the formula browser. Select
Mandelbrot in Standard.ufm, and then click Open. This creates a new default
Mandelbrot fractal.
1.
2.
(Note: Skip this step if you already have a fractal window open that you would like to
turn into an animation.)
Move the time slider at the bottom to the far right. This sets the current frame to 100.
(If you cannot see the time slider, click Animation Bar on the Options menu to reveal
it.)
Click the Animate button on the animation bar to turn Animate mode on. In Animate
mode, changes you make to the fractal are applied to the current frame only. This is
necessary because we want to keep frame 1 as it is, and change frame 100 to
something else.
3.
Note that the fractal window now shows red animation indicator marks in its corners,
and "(Animating)" in the title bar. This shows that Animate mode is on.
4.
Shift-click inside the fractal window, hold the mouse button down, and drag upwards to
zoom in. Release the mouse button when you are satisfied with the result. (See Normal
mode for more information about zooming.)
Congratulations! You have just made your first zoom movie. Drag the time slider to the
left and right to see a real-time preview.
5.
Note that above the time slider, two key icons have appeared, one at frame 1, and one
at frame 100. This shows that keys have been recorded at those frames.
6.
To make the movie more interesting, let us add a rotate effect. Move the time slider to
frame 50, and ensure that Animate mode is still on.
7.
Enter 90 in the Rotation Angle input box on the Location tab of the Layer Properties
tool window. This will rotate the fractal 90° clockwise at frame 50.
8.
Click the Animate button again to turn off Animate mode, because we are done
recording this animation for now. It is a good habit to leave Animate mode off normally
to avoid unintended changes to your animations.
Click the Play button on the Animation bar to start playing a preview of the animation,
or drag the time slider back and forth.
9.
Observe that the animation starts unrotated, rotates to 90° at frame 50, and then
rotates back to normal at frame 100, while zooming in all the time. The frames where
we did not explicitly set new values are interpolated to create a smooth animation.
Notes
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In Ultra Fractal, there is no fundamental difference between animations and still (normal)
fractals. A still fractal is simply a fractal without any animation keys. If you only want to
create still fractals, just hide the animation bar and ignore the Animation menu.
As you can see, the fractal does not interpolate from one set of parameters to another, like
in some other fractal programs. Instead, every parameter and setting has its own set of keys
and interpolates between them independently. This makes creating and editing animations
much easier and enables you to create more complex animations.
To create a movie clip of your animation, render it to disk.
Next: Animation keys
See Also
Tutorial: Working with animations
Animation
235
Animation keys
While you are creating animations, you are actually creating animation keys for the parameters that
are animated. The animation keys define how the values of those parameters change over time.
Each parameter that can be animated has its own list of animation keys, which is initially empty. In
this case, the parameter just has a static value that is the same for the entire frame range, and it is
not animated.
When you first change a parameter while Animate mode is on, Ultra Fractal inserts a new key for
that parameter at frame 1 with its old value. Then, it inserts a second key at the current frame with
the new value.
The time slider shows the keys as blue and yellow dots. Keys are displayed as yellow dots if they are
located at the current frame. In this example, if you now move the time slider from frame 1 to frame
50, the parameter animates from its old value to the new value.
Notes
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The key at frame 1 with the old value is only inserted when the parameter does not yet have
any keys. If the parameter already has one or more keys, Ultra Fractal only inserts a key at
the current frame.
If Animate mode is on, and you change a parameter that already has a key at the current
frame, Ultra Fractal adjusts the value of that key instead of inserting a new key.
Use the Timeline tool window to edit and delete keys. You can also delete the key at the
current frame from the right-click menu of an animated parameter. See Editing animations.
Internally, a key stores its position as a time value, not as a frame number. This makes it
possible to scale animations without introducing round-off errors. See Time settings.
Next: Animate mode
See Also
Tutorial: Working with animations
Editing animations
Animation
236
Animate mode
The Animate mode toggle controls what happens when you make changes to a fractal.
Set Animate mode on or off using the Animate button in the animation bar, the Animate
command on the Animation menu, or the F3 key.
By default, Animate mode is off. In this case, changes that you make to the fractal, such as zooming
in or adjusting a parameter, are applied to the entire range of frames. Changes never result in new
animation keys; they only adjust the existing keys or the static value of non-animated parameters.
If Animate mode is on, changes that you make are applied to the current frame only. Ultra Fractal
creates or adjusts keys at the current frame to accomodate your changes. This is the primary way to
animate parameters and therefore create animations.
While Animate mode is on, the corners of the fractal window are marked with red animation
indicators, and "(Animating)" is displayed in the title bar. Also, a small red animation indicator is
shown next to each parameter that can be animated. The indicator reminds you that keys will be
created or updated when you change that parameter.
If Animate mode is off, and you change a parameter that already has one or more keys, the values
for all keys are adjusted. For example, if you zoom in, the entire animation will be zoomed in; if you
apply a rotation, the entire animation will be rotated. This is very useful if you want to do global
adjustments. In practice, you will usually switch Animate mode on and off while working with an
animation to achieve the effects that you are after in an efficient way.
To adjust the values for all keys when Animate mode is off, Ultra Fractal calculates the
difference between the new value and the old value, and adds that to the values for all
keys. For floating-point parameters with exponential interpolation, however, Ultra Fractal
divides the new value by the old value and multiplies the values for all keys by the result.
Next: Animation bar
See Also
Tutorial: Working with animations
Animation
237
Animation bar
The animation bar at the bottom of the screen contains the time slider and provides quick access to
controls that you often use while working with animations.
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The button on the far left side hides or shows the animation bar. You can also click
Animation Bar on the Options menu.
The time slider sets the current frame. You can also enter the current frame directly in the
input box to the right of the time slider. To the right of that input box, the time between the
first frame of the animation and the current frame is shown, in hours, minutes, seconds, and
1/100 seconds.
Above the time slider, blue and yellow key icons indicate where keys have been inserted. A
key icon turns yellow when it is at the current frame. Click on a key icon to jump to that key's
frame.
The Animate button turns Animate mode on or off.
The Previous Key and Next Key buttons jump to the first key before or after the current
frame.
The Play button starts or stops real-time playback of the animation.
The Time Settings button opens the Time Settings dialog where you can scale the animation
and adjust its length.
The Timeline button activates the Timeline tool window where you can edit and delete
animation keys, and adjust interpolation curves.
Notes
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Although the position of keys are shown above the time slider, you cannot directly edit keys
from there. Use the Timeline tool window instead.
Most commands are also available on the Animation menu with keyboard shortcuts.
Next: Playing animations
See Also
Tutorial: Working with animations
Animation
238
Playing animations
While you are working with an animation, you will often want to see a quick live preview. You can
drag the time slider back and forth to slowly preview a part of the animation in the fractal window. If
the fractal is not too slow to calculate, you can also play a real-time preview in the fractal window.
Click the Play button in the animation bar to start or stop playing a preview of the
animation, or click Play on the Animation menu.
While playing the preview for an animation with multiple layers, Ultra Fractal gives some layers more
priority than others. The active layer is calculated with the highest priority, and then the other visible
layers are calculated from top to bottom, with the editable layers first. To speed up the preview, you
can temporarily hide one or more layers.
The preview is always played at a constant frame rate, independent of the frame rate of the
animation. Click Options on the Options menu and then click the Fractal tab to change the
Animation preview speed. Higher values give smoother animation, but allow less time per
frame, so individual frames will show less detail. The best value depends on the speed of
your computer and the complexity of the animations.
Notes
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Playback will not work well if the drawing method of a layer is set to One-pass linear. Use
Guessing or Multi-pass Linear instead.
To create a final movie clip of your animation, or to create a quick preview movie, render it
to disk.
Next: Animating locations
See Also
Tutorial: Working with animations
Rendering animations
Animation
239
Animating locations
Although you can do much more with animation in Ultra Fractal, the most obvious thing to animate is
the location of the fractal to create zoom movies. The location is controlled by five parameters on
the Location tab of the Layer Properties tool window: Center, Magnification, Rotation Angle, Stretch,
and Skew Angle.
To animate the location, first set Animate mode to on and move the time slider to the frame
where you want to create animation keys, as described in Creating animations.
Use the same zooming, panning, and rotation features that you would normally use (see
Normal mode and Select mode). They work the same as when Animate mode is off, except
that only the current frame is modified, instead of the entire range of frames.
If you use Select mode, Ultra Fractal always inserts keys at the current frame for all five location
parameters, even when the value of the parameter has not been changed. For example, if you just
zoom in without stretching or skewing, keys for Stretch and Skew will also be inserted although their
values have stayed the same. If you do not want this, use Normal mode instead.
Of course, you can also animate the location by changing one of the location parameters directly
while Animate mode is on. You can also edit the corner coordinate parameters in the lower half of
the Location tab, but this just indirectly changes the normal parameters in the upper half.
Always make sure whether Animate mode is on or off. If you zoom in while Animate mode is off, this
will transform the entire animation, which usually is not what you want.
The behavior of the Copy, Paste, and Reset buttons in the Location tab behave depends on
whether or not Animate mode is on, providing flexible ways to copy and clear animation keys. See
also Editing animations.
Animate mode on
Animate mode off
Copies the location at the current frame to
the Clipboard, without any animation keys.
Copies the location for the entire frame range
to the Clipboard, including all animation keys.
Sets the current location to the location on
the Clipboard, inserting animation keys
when necessary, just as if you entered
those values manually.
Sets the current location to the location on
the Clipboard, overwriting any animation
keys.
If the location on the Clipboard has no
animation keys (copied with Animate mode
on, or from a non-animated fractal), any
animation keys in the current location will be
removed.
You must turn off Animate mode before
pasting locations with animation keys
(copied when Animate mode is off).
Resets the location at the current frame to
the default location for the current fractal
formula, inserting animation keys when
necessary.
Next: Animating parameters
240
Clears all animation keys and resets the
location to the default location for the current
fractal formula.
See Also
Tutorial: Working with animations
Animate mode
Timeline
Animation
241
Animating parameters
You can animate almost anything in Ultra Fractal, including all formula parameters and settings such
as Maximum Iterations and Color Density.
To animate a parameter, first set Animate mode to on and move the time slider to the frame
where you want to create a new animation key, as described in Creating animations.
Parameters that can be animated will display a red animation indicator next to them while
Animate mode is on. Simply type a new value or use the Explore feature to change the
parameter.
A blue dot next to a parameter means that it is animated (i.e. has one or more animation keys). If
the blue dot turns into a yellow marker, this means that the parameter contains an animation key
at the current frame. In this case, editing the parameter while Animate mode is on will change the
value of the key at the current frame instead of inserting a new key.
If Animate mode is off, editing an animated parameter will adjust the values of all its animation keys.
For example, if a parameter animates from the value 1 at frame 1 to 4 at frame 100, and the
current frame is 1 and you change the value to 2, the value at frame 100 will change to 5. Floatingpoint parameters with exponential interpolation, such as Magnification and Color Density, are scaled
instead of translated.
Complex, floating-point, and integer parameters will be interpolated smoothly between animation
keys. You can also animate enumerated and boolean parameters, but they will not be interpolated.
Right-click a parameter for a menu with options to insert a new key at the current frame or to
remove the existing key, and to jump to the previous and next key for that parameter. See Editing
animations.
Inserting a key manually is useful if you want to animate a parameter from frame 20 to
frame 30, for example. If you just move the time slider to frame 30 and change the
parameter, the parameter will be animated from frame 1 to frame 30, which is not what
you want.
Instead, first move the time slider to frame 20 and insert a key there (which does not
change the value of the parameter). Then move to frame 30, turn Animate mode on, and
edit the parameter to animate it.
Next: Animating gradients
See Also
242
Tutorial: Working with animations
Animating locations
Timeline
Animation
243
Animating gradients
Of course, you can also animate gradients in Ultra Fractal to create color cycling movies or subtle
color change effects during your animations.
The gradient editor contains a small bar just above the rotation slider that shows whether or not the
control points above it are animated. When Animate mode is on, this bar shows red animation
indicators below each control point to illustrate that it can be animated.
To animate a control point, first set Animate mode to on and move the time slider to the
frame where you want to create a new animation key, as described in Creating animations.
Now simply drag the control point around. This will record keys for both the color and the
position of the control point. You can also type new values in the input boxes in the gradient
editor. See also Editing gradients.
As with parameters, a blue dot below a control point means that a control point is animated. It
turns into a yellow marker if the control point has an animation key at the current frame. In this
case, dragging the control point while Animate mode is on will change the value of the keys at the
current frame instead of inserting new keys.
If Animate mode is off, dragging an animated control point will transform the values of all its
animation keys. For example, if a control point animates from position 0 at frame 1 to 50 at frame
100, and the current frame is 1 and you drag it to position 20, its position at frame 100 will change
to 70.
The following gradient adjustment options record keys when Animate mode is on and can be used to
create animated gradients: Randomize Custom (if Randomize control points is not checked),
Adjust Colors, Reverse, and Invert.
The Randomize, Randomize Bright, and Randomize Misty options clear all control points and
then generate a new gradient, so they cannot animate the existing control points.
The Copy and Paste commands work differently depending on whether or not Animate mode is on:
Animate mode on
Animate mode off
Copies the control points at the current
frame to the Clipboard, without any
animation keys.
Copies the control points for the entire frame
range to the Clipboard, including all animation
keys.
244
Pastes the control points from the Clipboard
into the gradient, inserting animation keys
as necessary.
If the number of control points on the
Clipboard is equal to the number of control
points in the gradient, this will animate the
control points in the gradient.
You must turn off Animate mode before
pasting gradients with animation keys
(copied when Animate mode is off).
Pastes the control points from the Clipboard
into the gradient, overwriting any animation
keys.
If the gradient on the Clipboard has no
animation keys (copied with Animate mode
on, or from a non-animated gradient), any
animation keys in the gradient will be
removed.
Notes
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You can create color cycling animations simply by changing the Rotation setting or
dragging the rotation slider while Animate mode is on.
The individual input boxes in the gradient editor do not show animation indicators. Refer to
the animation indicators in the horizontal bar below the control points instead.
You cannot directly insert or delete animation keys in the gradient editor. Use the Timeline
tool window instead.
Because each control point is animated separately, you cannot create an animation from one
arbitrary gradient to another, and you cannot animate the insertion or deletion of a control
point. To blend from one arbitrary gradient to another, duplicate the current layer, change
the gradient on the new layer, and animate the opacity of the layer so it fades in to replace
the original gradient.
Next: Animating layers
See Also
Tutorial: Working with animations
Animating parameters
Gradients
Animation
245
Animating layers
Animating the opacity and blending of layers is the way in Ultra Fractal to animate blends between
different fractals, gradients, color combinations, and so on.
To animate layer blending, first set Animate mode to on and move the time slider to the
frame where you want to create new animation keys, as described in Creating animations.
Now simply drag the opacity slider to a new value, or set a new merge mode.
As with any parameter, a blue dot next to the Merge Mode input box or the opacity slider means
that it is animated. It turns into a yellow marker if there is an animation key at the current frame.
In this case, editing the parameter while Animate mode is on will change the value of the key at the
current frame instead of inserting a new key.
Notes
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If you animate the merge mode, it will not be interpolated between animation keys, which
gives sudden changes. For smooth transitions, create two identical layers, one with the first
merge mode, and one with the second, and animate the opacity of both layers to create a
smooth transition between the two.
You cannot animate the visibility or the insertion or deletion of a layer. Instead, animate the
opacity to 0% so the layer appears to be hidden.
You also cannot animate a layer from or to a mask layer. Instead, animate the opacity part
of the gradient of the mask layer to be 100% opaque (white) so the mask has no effect.
Next: Time settings
See Also
Tutorial: Working with animations
Animating parameters
Layers
Animation
246
Time settings
Each fractal starts with 100 frames and a frame rate of 30 frames per second, but you can of course
easily change the length and the frame rate of the animation.
Click the Time Settings button on the animation bar, or click Time Settings in the
Animation menu. This opens the Time Settings dialog where you can extend, reduce, or
scale the animation.
The Time Settings dialog enables you to enter new values for the number of frames and the current
frame rate (in frames per second). The total time for the animation is also shown and updated as
you type, according to the following formula:
Time (seconds) = Frames / Frame Rate (fps)
Before you enter a new frame rate, review the Lock frames and Lock time radio buttons. If Lock
frames is checked, the number of frames will not be changed, so the total time of the animation will
change according to the new frame rate. Otherwise, the number of frames will be adjusted as you
type in order to preserve the duration of the animation.
With the radio buttons in the Existing keys group, you can globally scale the existing animation
keys according to the new length in frames.
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If Scale to new length is checked, the animation keys will be scaled such that their relative
positions in the animation do not change. For example, if you have keys at frame 1 and 50
and the number of frames changes from 100 to 200, the keys will end up at frame 1 and 99,
so they stilll occupy the same part of the animation.
If Keep at first frame is checked, the frame number of the animation keys will stay the
same. If the number of frames is increased, this will leave the new part of the animation
empty so you can add new animation keys at the end. If the number of frames is decreased,
the last part of the animation will be chopped off (but not deleted; you can still work with it
in the Timeline tool window).
If Keep at last frame is checked, the frame number of the animation keys will be adjusted
to keep the distance to the end of the animation the same. If the number of frames is
increased, this will move the existing keys to the end, so you can add new keys at the
beginning. If the number of frames is decreased, the first part of the animation will be
chopped off (but not deleted; you can still work with it in the Timeline tool window).
Notes
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Because the position of an animation key is internally stored as a precise time value, you can
scale an animation more than once without introducing round-off errors. For example, if you
reduce an animation with 100 frames to 10 frames with Scale to new length checked, a
key at frame 25 will end up at frame 3. If you now scale the animation back to 100 frames,
the key will be back at frame 25.
For more information on individual controls in the Time Settings dialog, click the
button in
the title bar, and then click a control.
You can change the default fractal to have a different length and frame rate. See Default
fractal.
Next: Editing animations
See Also
247
Tutorial: Working with animations
Creating animations
Animation keys
Animation
248
Editing animations
Ultra Fractal provides various ways to edit and change your animations after you have initially
created them. Often you will use the Timeline tool window, which also reveals the structure of your
animation. But you can also directly work with animation keys by right-clicking on animated
parameters, which opens a menu with animation-related commands. This can be useful for small
changes.
To insert a new key at the current frame, right-click a parameter and click Insert Key.
To delete a key at the current frame, right-click a parameter and click Delete Key. Use the
Timeline tool window to delete multiple keys at once.
To jump to the first key before the current frame, right-click a parameter and click Previous
Key.
To jump to the first key after the current frame, right-click a parameter and click Next Key.
Note that the Previous Key and Next Key commands in the right-click menu for a parameter jump
to the previous and next keys for that parameter only. To jump to the previous and next keys in the
entire animation, use the global commands in the animation bar or on the Animation menu instead.
A powerful way to make global changes to an animation is to copy and paste parts of it, using the
Copy and Paste commands found everywhere in Ultra Fractal. You can copy locations,
transformations, formulas, coloring settings, gradients, layers, and even entire fractals. The behavior
of the Copy and Paste commands depends on whether or not Animate mode is on.
Animate mode on
Animate mode off
Copies the settings at the current frame to
the Clipboard, without any animation keys.
Copies the settings for the entire frame range
to the Clipboard, including all animation keys.
Copies settings from the Clipboard,
inserting animation keys when necessary,
just as if you entered all values manually.
Copies settings from the Clipboard,
overwriting any animation keys.
If the settings on the Clipboard have no
animation keys (copied with Animate mode
on, or from a non-animated fractal), any
existing animation keys will be removed.
You must turn off Animate mode before
pasting settings with animation keys
(copied when Animate mode is off).
Remember: if Animate mode is on, your actions only affect the current frame; if Animate mode is
off, your actions are applied to the entire fractal.
Next: Timeline
See Also
Tutorial: Working with animations
Animation keys
Time settings
Animation
249
Timeline
The Timeline tool window provides the most versatile way of editing your animations. It shows a tree
view of all parameters in the fractal, grouped by layer and category, with an overview of their
animation keys.
To open the Timeline tool window, click the Timeline button on the animation bar, or click
Timeline on the Animation menu.
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The tree view on the left displays all layers of the active fractal window. Within each layer,
the parameters are grouped by categories that correspond to the tabs of the Layer Properties
tool window, combined with layer settings and the gradient.
The time view on the right displays the animated range and animation keys for all
categories and parameters. The animated range of a category contains the animation keys of
all parameters within the category.
The selection properties at the bottom enable you to edit the current selection. For
animated ranges, you can change the begin and end frames, which scales the range. For
animation keys, you can change the value of the key and its frame. You can also select how
Ultra Fractal interpolates around the key with various interpolation options. See
Interpolation.
It is easy to discover which parts of a fractal are animated by looking at the animated ranges for
different categories. To move a complete animated range, grab it in the middle and drag it to the
left or to the right. To resize an animated range, drag the resize gribs at the left or right ends. This
powerful way to edit animations adjusts all animated keys within the category that corresponds with
the animated range.
You can also click on a single animation key and move it, or adjust its value with the selection
properties panel at the bottom. To select multiple keys or ranges, hold down Ctrl while you click.
Hold down Shift to select a consecutive area of keys or ranges. This enables you to move or resize
multiple items at once.
250
To insert a new key, click the Insert button and then click in the time view where you want
to create a new key.
To delete the currently selected key or animated range, click the Delete button.
Click the Zoom In button to enlarge the area with frames at the center of the time view, so
you can work more accurately.
Click the Zoom Out button to be able to see more frames at the same time.
To scale the time view such that all frames of the animation will just fit in the currently
visible area, click the Reset View button.
Notes
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To quickly insert or delete keys, hold down Ctrl and click in the time view where you want to
create a new key, or on the key that you want to delete.
Right-click in the time view for a menu with frequently used commands.
Next: Interpolation
See Also
Tutorial: Working with animations
Time settings
Editing animations
Animation
251
Interpolation
To create smooth animations, Ultra Fractal automatically interpolates between the animation keys
that you have recorded. By default, a smooth interpolation method is used that damps sudden
changes and creates smooth ease-in and ease-out effects around each key. However, you can select
different interpolation methods for each animation key using the Timeline tool window.
There are three interpolation methods available:
To adjust interpolation methods for an animation key, select the key in the Timeline tool window.
The properties panel at the bottom now shows the frame, the value, and the current interpolation
settings for the key.
You can set the interpolation method for both the curve to the left and the curve to the right of the
key. In some cases, this will also change the interpolation settings for adjacent keys. For example, if
you set the interpolation method for the curve to the right of the current key to No, the interpolation
method for the curve to the left of the next key will also be set to No.
Sets No interpolation. The value of the parameter will remain the same until it suddenly
jumps to the value of the next key.
Sets Linear interpolation. The value of the parameter will linearly change from one key to
the next. This can result in noticeable changes in the speed at which the parameter changes
around animation keys. If you want to create seamlessly looping animations with rotation, for
example, you need to use linear interpolation to keep the rotation speed constant.
Sets Smooth interpolation. The value of the parameter will gradually change from one key
to the next, slowing down and speeding up where needed to avoid sudden changes in the
speed at which the parameter is changed. This is the default interpolation method.
Next: Exponential interpolation
See Also
Tutorial: Working with animations
252
Timeline
Animation
253
Exponential interpolation
For floating-point parameters, Ultra Fractal offers an additional interpolation setting called exponential interpolation.
This can be set independently of the normal interpolation methods in the Timeline tool window.
Exponential interpolation should be used for parameters that are exponential in nature. This means that in order to
experience the same apparent increase of the parameter, you need to double it each time, instead of adding something.
A perfect example is the Magnification parameter on the Location tab. It starts at 1. If you add 1 to make it 2, the fractal
is magnified by a factor of two. If you add 1 again, the fractal is magnified by only a factor of 1.5. If you keep adding 1,
the apparent difference gets less and less. At a magnification of 1000, you will probably not notice it if you change the
magnification to 1001. In contrast, if you keep multiplying the magnification with two, you will each time experience the
same zoom effect. Clearly, the Magnification parameter is exponential in nature. In contrast, the Rotation Angle
parameter is linear in nature.
This is important when interpolating animations, because exponential parameters must also be interpolated
exponentially. For example, if you create an animation of 99 frames where Magnification ranges from 1 at frame 1 to 16
at frame 99, it must be 4 at frame 50 to give the effect of a gradually increasing zooming level. With normal
interpolation, it will be 8.5. Fortunately, the Magnification parameter uses exponential interpolation by default.
To turn exponential interpolation on and off for a parameter, open the Timeline tool window, select the parameter in the
tree view, and click the Exponential interpolation check box.
Notes
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Certain built-in parameters in Ultra Fractal, such as Magnification, Stretch, and Color Density in the Inside and
Outside tabs, are exponential by default. When you are writing a formula, you can also specify whether or not
floating-point parameters in your formula should be treated as exponential by default. See the exponential
setting.
Due to the nature of exponential values, exponential interpolation only works if both the begin and end points are
nonzero and both positive or negative.
See Also
Tutorial: Working with animations
Timeline
Interpolation
Animation
254
Browsers
To explore and organize the various types of fractal-related files on your computer, Ultra Fractal
includes a flexible file browser. It works much like Windows Explorer, but it also works with files
containing multiple entries, such as parameter files or formula files.
To open a browser, click Browse on the File menu.
The browser is divided into four panes:
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The location input box at the top shows the file or folder that is currently selected. You can
also type a new location here. Click the Up button next to the location input box to go up to the
parent folder.
The tree on the left shows an overview of all files and folders on your computer. If Library
mode is active, only the files and folders in the library of the current file type are shown. See
Library mode.
The list on the right shows the contents of the file or folder selected in the tree. The name of
this file or folder is displayed by the location input box. The list can show either item details,
icons or thumbnails. See View style.
The code preview shows the text corresponding to the entry selected in the list.
The image preview shows a preview image for the entry selected in the list.
Next: Browser toolbar
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See Also
Quick Start Tutorial
Modal browsers
Formula ratings
Workspace
Fractal windows
256
Browser toolbar
The toolbar for the browser contains commands to view and work with folders, files and entries:
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The New button creates a new fractal from scratch.
The Open button opens a file from disk.
The Browse button opens a new modeless browser. To duplicate the browser, click Duplicate
on the File menu.
The Cut, Copy, and Paste buttons are used to move and copy selected files, entries, and
folders. See Organizing your work.
The Delete button deletes selected files, entries, and folders.
The Find Entries button opens a dialog where you can search for entries (such as parameter
sets and fractal formulas) on your computer. See Finding files and entries.
The Library Only button toggles library mode on and off. See Library mode.
The View button selects the current view style: details, icons or thumbnails. See View style.
The File Type drop-down box selects which files are currently visible. See File types.
The commands on the toolbar are duplicated on the File, Edit, and View pull-down menus. Frequently
used commands are also on the menu that pops up when you right-click in the browser.
Next: Modal browsers
See Also
Keyboard shortcuts for browsers
Browsers
Workspace
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Modal browsers
There are two types of browsers: modeless and modal browsers. A modeless browser is created
when you click Browse on the File menu. Modeless browsers are typically used to organize files. They
can stay open in the background while you work with other windows, such as fractal windows.
A modal browser is shown when you must select a parameter set or formula. The modal browser
looks like a modeless browser, but it contains a small built-in toolbar, and Open and Cancel buttons.
You must close the modal browser by clicking Open or Cancel before continuing.
Modal browsers are also used to save parameter sets and gradients. In this case, they contain input
boxes to enter a file name and a title, and a Save button.
You can compare modal browsers to standard Windows Open and Save dialog boxes, except that
they work with entries (such as parameter sets and formulas) instead of files. In the same way, a
modeless browser can be compared to Windows Explorer.
Next: File types
See Also
Browsers
Browser toolbar
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File types
The browser works with all Ultra Fractal file types. You can set it to display all fractal-related files, or
only files of a selected type.
To select a file type, click File Types on the View menu, and then click the file type. You can also use
the drop-down box on the toolbar. The following file types are available:
Fractal Files
Displays fractal files (*.ufr). Fractal files contain complete fractals.
See Opening and saving fractals.
Parameter Files
Displays parameter files (*.upr). Parameter files contain multiple
parameter sets that describe a fractal without storing the calculated
pixels. Older Fractint parameter files (*.par) are also shown. See
Parameter files.
Gradient Files
Displays gradient files (*.ugr). Gradient files contain multiple
gradients that store coloring information for a fractal. Older gradient
files (*.ual) and Fractint palette files (*.map) are also shown. See
Opening and saving gradients.
Transformations
Displays transformation files (*.uxf). Transformation files contain
multiple transformation formulas. See Transformations.
Fractal Formulas
Displays fractal formula files (*.ufm). Fractal formula files contain
multiple fractal formulas. Older Fractint formula files (*.frm) are also
shown. See Fractal formulas.
Coloring Algorithms
Displays coloring algorithm files (*.ucl). Coloring algorithm files
contain multiple coloring algorithms (formulas). See Coloring
algorithms.
Classes
Displays class library files (*.ulb). Class library files contain multiple
classes, which can be used in formulas to extend their behavior. See
About classes.
Select All Files to display all these file types at the same time.
Notes
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If All Files is selected, Library mode is not available.
Modal browsers cannot switch between file types, since their purpose is to open or save a file
of a particular type.
Next: Library mode
See Also
Browsers
259
Browser toolbar
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Library mode
The browser can be switched to library mode. In library mode, only the files and folders within the
library of the visible file type are shown.
This prevents cluttering the tree on the left side of the browser with all folders on your computer
(most of which will not contain any fractal-related files), and makes it easier to work with parameter
files, gradient files, and formulas.
To activate library mode, click Library Only on the View menu. Click it again to turn library
mode off.
The library for each file type is a folder (for example Documents\Ultra Fractal 5\Parameters) that
contains files for that file type by default.
Usually, you will work in library mode, but if you want to open a file or entry that is not in the library,
you have to turn library mode off in order to find it. In this case, you can view all files and folders on
the local drives (including network drives) on your computer.
Notes
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Library mode does not work when all file types are visible, because files of different types do
not share the same library folder.
The location of the library of a file type can be set in the Folders tab of the Options dialog.
To open a file located on a different (networked) computer, you have to map a shared folder
on that computer to a network drive with Windows Explorer first.
Next: View style
See Also
Browsers
Browser toolbar
261
View style
The list of items in the browser can display the items with different view styles, just like in Windows
Explorer.
To change the view style, click a new view style on the View menu. You can also click the View
button on the tool bar and then click a view style on the pop-up menu that appears.
Click Thumbnails to display the items as large thumbnails that contain a preview of the
item.
Click Large Icons to display the items as a collection of large icons, where each icon shows
the type of the item rather than a preview.
Click Small Icons to display the items as a collection of small icons.
Click List to display the items as a list of small icons.
Click Details to display the items in a list with columns that contain more information on
each item, such as the date, author and comments. You can click on a column header to sort
the items by the information in that column. Next to Thumbnails, this is probably the most
useful view style.
In Thumbnails view, the browser caches the thumbnails that it generates for parameter files, fractal
files and formulas. These are stored in the preview cache that is also used for the preview window
in the bottom-right corner of the browser.
You can adjust the size of the preview cache in the Browser tab of the Options dialog. If you have
many parameter sets that you view regularly, you might want to increase the cache size, although
this uses more space on your hard disk. You can also turn off thumbnail caching for formulas to
leave more space in the cache for parameter and fractal thumbnails which are more timeconsuming to regenerate.
Next: Opening files and entries
See Also
Browsers
Browser toolbar
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Opening files and entries
Browsers are used to organize your work, but they can also open all types of files and entries. (This
does not apply to modal browsers.)
To open a file or entry, double-click in the list on the right of the browser. If you double-click a
folder, its contents will be shown.
Fractal files and parameter sets will be opened in a new fractal window. You can also drag
them from the browser to any open fractal window.
Right-click on a fractal file, parameter file, or parameter set and click Render to Disk to
render it to disk. You can also drag them to the Render to Disk tool window.
Right-click a parameter set and click Open as Text to open the parameter set in the
formula editor to edit it manually.
Gradients will be opened in a new gradient editor. You can also drag them from the browser
to any open gradient editor.
Transformations, fractal formulas, coloring algorithms and classes will be opened in the
formula editor.
You can also drag transformations to the list of transformations in the Mapping tab of the
Layer Properties tool window. Fractal formulas can be dropped on the top of the Formula
tab, and coloring algorithms can be dropped on the top of the Inside and Outside tabs to
select them.
Next: Organizing your work
See Also
Browsers
Browser toolbar
Modal browsers
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Organizing your work
To organize your fractal-related files, you can move, copy, delete, and rename files and entries in the
browser. Again, the browser works similar to Windows Explorer, except that it also manipulates the
entries in parameter files, gradient files, and formula files.
To move a file, folder, or entry, select it in the list view, and click Cut on the Edit menu.
Select the new location, and then click Paste on the Edit menu.
To copy a file, folder, or entry, select it in the list view, and click Copy on the Edit menu.
Select the new location, and then click Paste on the Edit menu.
Click Paste on the Edit menu to move or copy an item that was previously cut or copied to
the Clipboard.
To delete a file, folder, or entry, select it in the list view, and click Delete on the Edit menu.
To rename a file, folder, or entry, select it in the list view and click it again, or click Rename
on the Edit menu.
These commands are also on the menu that pops up when you right-click an item in the list view or
in the tree view. In this way, you can also move, copy, delete, and rename files and folders using the
tree view.
Alternatively, you can drag items from one location to another to move them. Hold down Ctrl while
dropping to copy the items instead.
Notes
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Items that are cut or copied to the Clipboard are not actually moved or copied until you use
the Paste command.
Deleting a file, entry, or folder will delete it immediately. It will not be moved to the Recycle
Bin.
Next: Finding files and entries
See Also
Browsers
Browser toolbar
264
Finding files and entries
The browser can search for files and entries that match various criteria that you specify. This is
useful when you are looking for certain formulas, parameter sets, or gradients, but you do not know
their exact name or location.
To search for files and entries, click Find Entries on the Edit menu. This will open the Find
Entries dialog box.
The Find Entries dialog box allows you to search for parameter sets, gradients, and formulas by title,
comments, and identifier. You can also specify selected files and folders to search.
For parameter sets, you can also search for authors and formulas (identifiers and files) that are
used.
Click Find Now to start the search. This will populate the list in the dialog box with results. Click a
result to open it in the browser. The Find Entries dialog box will stay on top of the browser until you
close it.
Tip: When you open the Find Entries dialog box while selecting a class for a class parameter, it will
only display classes that are valid for that class parameter. If you don't enter any criteria, the list of
results will show all matching classes in the formula library, which can be very useful.
Next: Formula ratings
See Also
Browsers
Browser toolbar
265
Formula ratings
To help you to quickly see which formulas you should try first, Ultra Fractal contains a simple formula
rating system. This divides all formulas into three categories:
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Recommended
These formulas are the most versatile, or easiest to use. Try these first.
Average
All other formulas. They may be very worthwhile, but are perhaps not the first choice when
you are new to Ultra Fractal or to a certain formula file.
Not recommended
These formulas may be obsolete or replaced by a newer formula.
Both individual formulas and entire formula files can be rated. In the browser, the formula icon
shows the rating, as shown below:
Recommended formulas, such as Standard.ufm, have a little star in their icon, while formulas that
are not recommended (Fractint.ufm) are greyed out slightly. All other formulas have their normal
icon, such as My Formulas.ufm in the screen shot above.
By default, the browser groups formulas by rating. Click Group By Rating on the View menu to turn
this on or off.
Ratings for formulas are updated automatically when you update the public formulas. However, you
can also add your own ratings which will not be overridden by the public ratings. Select the items to
want to rate in the browser, right-click them to open a pop-up menu, click Rating, and then click
the desired rating.
How do formula ratings work?
Formula ratings are stored in two text files: the private ratings file in the main Formulas folder,
and the public ratings file in the Formulas\Public folder. Both are called Ratings.txt. The public
ratings file is automatically updated when new public formulas are downloaded. The private ratings
file contains your own ratings that you have added via the Rating menu item of the pop-up menu in
the browser.
In addition, formulas can also store their own rating. This is a way for formula authors to indicate
which are recommended formulas in their formula files. (See the rating setting.)
If you have rated a formula yourself (so it is in the private ratings file), Ultra Fractal uses that.
Otherwise, it uses the rating that is stored in the formula file. If the formula file doesn't contain a
rating, it uses the rating from the public ratings file. This means that formula authors can override
the public ratings in their own formula files, and you can in turn override those ratings.
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For formula files, this works the same, except that there are no ratings stored in the formula file:
there are only the private and public rating files. In this case, Ultra Fractal uses the public ratings
unless you have defined your own rating.
Currently, the public ratings are created by the formula database administrator, so this is not a
public voting system. If you feel your formulas are rated incorrectly, please contact the rating
administrator via [email protected]
See Also
Browsers
Formulas
Public formulas
rating setting
267
Formula editors
Ultra Fractal contains a built-in formula editor. It is a powerful text editor with syntax highlighting and extra productivity
features for writing formulas efficiently.
The toolbar contains commands to edit and save the file you are working on:
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The New button creates a new fractal from scratch.
The Open and Browse buttons open files from disk.
The Save button saves your changes to disk.
The Undo and Redo buttons undo changes you have made to the file.
The Cut, Copy, and Paste buttons are used to move and copy blocks of text. See Editing formulas.
The Find button opens a standard Find dialog where you can search for text.
The Find Entries button opens a dialog where you can search for formulas in the file. See Finding text and
formulas.
The Active Formula drop-down box shows the formulas in the file and allows you to quickly jump to any formula.
The New Formula button adds a new empty formula to the file.
The Complete Template button completes the editor template at the cursor position. See Templates.
The commands on the toolbar are duplicated on the File, Edit, and Insert pull-down menus. Frequently used commands are
also on the menu that pops up when you right-click inside the editor.
Next: Editing formulas
See Also
Keyboard shortcuts for formula editors
Fractal formulas
Coloring algorithms
Transformations
268
Editing formulas
To edit a formula, open it in the built-in formula editor. Either:
Click the Edit button on the Mapping, Formula, Inside, or Outside tabs on the Layer
Properties tool window to edit the selected transformation, fractal formula, or coloring
algorithm. To edit a class, hold down the Browse button for the class parameter and then
click Edit.
Click Browse on the File menu to open a new browser, and double-click on a formula to edit
it.
Click Open on the File menu and select a formula file to open it in the formula editor.
The editor works similar to other Windows text editors and supports common text editor features:
Click Cut on the Edit menu to move the selected text block to the Clipboard.
Click Copy on the Edit menu to copy the selected text block to the Clipboard.
Click Paste on the Edit menu to insert the text on the Clipboard into the file at the position
of the cursor.
Click Undo on the Edit menu to undo your last change.
Click Redo on the Edit menu to cancel the last Undo command.
If you are editing a formula that is being used by an open fractal window, you can easily view your
changes:
Click the Reload button on the Mapping, Formula, Inside, or Outside tabs on the Layer
Properties tool window to save the formula file, recompile the formula, and recalculate the
layer in one step.
The formula editor makes it easy to navigate through large formula files:
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The drop-down input box in the toolbar lists all formulas in the file, sorted by identifier.
Simply click on a formula to jump to its first line.
Within a formula, click Next Section or Previous Section on the Edit menu to go to
different sections in the formula quickly.
Click Go to Line on the Edit menu to jump to a specific line number in the file.
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Notes
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Press F1 or click Help on the Help menu to get help on the word at the cursor position.
This works for reserved words, built-in functions, predefined symbols, settings, compiler
directives, and labels.
Click Check Class Syntax on the File menu to check all classes in the formula file for
errors. Errors and warnings are displayed in the Compiler Messages tool window. (To check
formulas in a file for errors, just load the file in the browser in thumbnail mode to see
which formulas will not load.)
In the status bar, the status of the file and the current row and column are displayed while
you type.
You can change the colors for various syntax elements in the formula editor on the Syntax
tab of the Options dialog.
Next: Finding text and formulas
See Also
Formula editors
Keyboard shortcuts for formula editors
Writing formulas
270
Finding text and formulas
The formula editor provides various ways of finding text and formulas within formula files:
Click Find on the Edit menu to search for text using a standard Find dialog. Click on the Find
Next button to start the search from the cursor position. The first occurrence of the text will
be highlighted. Since the Find dialog will stay on top of the editor, you can keep it open
while you edit the file.
Click Replace on the Edit menu to search for and replace text.
Click Find Formulas on the Edit menu to open the Find Formulas dialog. This dialog allows
you to search for formulas within the file, based on various criteria. Click the Find Now
button to start the search. Click a formula in the list of results to jump to it in the editor,
where you can review and edit it. The Find Formulas dialog will stay on top of the editor until
you close it.
Next: Indenting and commenting
See Also
Formula editors
Keyboard shortcuts for formula editors
Writing formulas
271
Indenting and commenting
The formula editor can indent and outdent blocks of code for you. Indentation is used to indicate the
logical structure of code, to make formulas easier to read.
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Click Indent Block on the Edit menu to move the selected lines to the right. This will add a
space at the start of each line.
Click Outdent Block on the Edit menu to move the selected lines to the left. This will
remove a space from each line, if there is one.
You can also easily comment and uncomment blocks of code. The compiler will ignore commented
code, so this is an easy way to (temporarily) disable parts of a formula.
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Click Comment Block on the Edit menu to comment the selected lines. This will put a
semicolon and a space at the start of each line.
Click Uncomment Block on the Edit menu to uncomment the selected lines. This will
remove a semicolon and a space from each line, if any.
Next: Templates
See Also
Formula editors
Keyboard shortcuts for formula editors
Writing formulas
272
Templates
To write formulas efficiently, you can use editor templates. An editor template is a commonly used
piece of code that can be inserted easily.
Click Complete Template on the Insert menu (or press Ctrl+J) to expand the pattern at
the cursor position to a template.
For example, to insert a parameter definition, enter "p" and press Ctrl+J. The pattern "p" will be
expanded to a default parameter definition:
param |
caption = ""
endparam
where | indicates the position of the cursor, so you're ready to type the name of the parameter.
If the pattern is not unique (for example when there are multiple patterns starting with "p"), a dialog
box is shown where you can select the desired template.
Go to the Editor tab in the Options dialog to see the default patterns and templates and customize
them.
See Also
Formula editors
Keyboard shortcuts for formula editors
Writing formulas
273
Exporting and rendering
To use the artwork that you create in Ultra Fractal for printing or on the web, you have to export it
or render it to disk. This will create a bitmap image of the fractal, ready for further processing.
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You can directly export the image from a fractal window to a bitmap image. Click Export
Image on the File menu, enter a file name, and click Save. See File formats for a
description of the image file formats that are supported.
Usually though, you will want to render your artwork to disk. Rendering to disk provides the following
benefits:
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Anti-aliasing for improved image quality. This is especially important if you are preparing
images for the web. See Anti-aliasing.
More accurate color blending and merging. When a fractal is rendered to disk, the colors are
calculated more accurately than the fractal window does, producing smoother, higher quality
images.
Support for large images. You can render images up to 100,000 by 100,000 pixels. Because
the images are rendered to disk, the size is not limited by available memory (RAM).
Entire parameter files can be rendered to disk with one command, producing multiple
images.
For animations, rendering is essential, since these cannot be exported normally.
Notes
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Exporting and rendering a fractal only saves the fractal as a bitmap image. You cannot open
this image in Ultra Fractal. Always save your fractal as a parameter set or a fractal file as
well to be able to open it in Ultra Fractal later.
To export a fractal as an image, you can also click Copy Image on the Edit menu. See
Copying and pasting fractals.
If you are using an evaluation copy of Ultra Fractal, exported and rendered images will be
marked with Evaluation Copy text. To fully enable exporting and rendering images, you must
purchase your copy of Ultra Fractal. See Purchasing Ultra Fractal.
Next: Rendering images
See Also
Tutorial: Learning about transformations
Tutorial: Masking
Render jobs
Fractal windows
274
Rendering images
Rendering fractals to disk is the preferred way of exporting your artwork to bitmap images, ready for
printing or publishing on the web.
To render the fractal in an open fractal window to disk, click Render to Disk on the Fractal
menu.
Click the Add button on the Render to Disk tool window to render a parameter set to disk.
Hold down the button and click Add Fractal to specify a fractal file to render.
This will open the Render to Disk dialog box. Here, you can specify a file name and file format for the
image, the desired size and resolution, and the anti-aliasing settings. To get help on a control in the
dialog box, click the ? button in the title bar, and then click the control.
Click OK to start rendering the fractal. This will create a new render job that starts calculating the
image in the background. Render jobs can be monitored and managed in the Render to Disk tool
window. See Render jobs.
Notes
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You can also render fractals and parameter sets directly from the browser by right-clicking
them and clicking Render to Disk, or by dragging them from the browser to the Render to
Disk tool window. See Opening files and entries.
The resolution specified when starting a render job is used to calculate the desired size in
pixels if you enter the width and height of the image in cm or inches. See Resolution.
When rendering very large images, you can use the Split into tiles option to automatically
split the rendered image into multiple rectangular tiles, labeled A1, A2, B1, B2, and so on.
This helps to keep the size of the individual image files at a reasonable level for any postprocessing. You can later stitch the tiles together with software such as Adobe Photoshop.
Check the Force Linear drawing method option for the highest image quality. This forces
Ultra Fractal to use the One-pass linear option as the drawing method in all layers of the
fractal to be rendered. In this way, you can work on the fractal with the Guessing drawing
method for convenience without having to change the drawing method for a final render.
Always save your fractals as a parameter set or a fractal file as well. Rendered images do not
contain any fractal information and Ultra Fractal will not be able to open them later.
Next: Rendering animations
See Also
Exporting and rendering
275
Rendering animations
Note: You need Ultra Fractal Animation Edition to render animations.
To create a final version of a fractal animation, you have to render it to disk. This works the same as
rendering images, except that the Render to Disk dialog shows additional options that are specific to
animations.
To render the animation in an open fractal window to disk, click Render to Disk on the
Fractal menu.
The Render to Disk dialog opens. Here, you can specify a file and file format for the animation. You
can either render the animation to an AVI movie, or to a sequence of bitmap images in any format.
It is recommended to render to a sequence of images for final renders. When you later want to
compress these to a single movie (for example in MPEG format) with programs such as VirtualDub, it
is much less time-consuming to experiment with different compression settings.
Apart from the regular settings such as the desired size and resolution and the anti-aliasing settings,
the dialog also provides specific settings for animations. You can select which frames you want to
render: the entire animation, the current frame, or a consecutive range of frames. When you are
rendering to a sequence of images, you can optionally offset the frame number of the generated
images. This is useful if you are dividing a long animation into several parts that are rendered
individually. To get help on a control, click the ? button in the title bar, and then click the control.
You can also apply motion blur to the rendered animation. The motion blur feature examines the
amount of movement in each frame and blurs it accordingly, like a film camera would. This makes
the movement in animations more natural and convincing.
Click OK to start rendering the animation. This will create a new render job that starts calculating the
image in the background. Render jobs can be monitored and managed in the Render to Disk tool
window. See Render jobs.
Notes
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It is recommended to use both anti-aliasing and motion blur when rendering animations to
reduce the amount of jumping and flickering pixels.
Motion blur is calculated directly from the coordinate movement that occurs when the fractal
is zoomed or rotated, and therefore it is efficient to calculate and fairly accurate. The
downside is that it only works with zooming, panning, rotating, and so on, and not with
movements that are the result of changes to other parameters.
Motion blur needs extra memory and temporary disk space, and because of this there is a
limit to the maximum size of the image that does not normally apply to disk rendering. For
example, a 1024x768 image takes 24 MB and a 4096x4096 image takes 512 MB of RAM.
Next: Rendering parameter files
See Also
276
Animation
Working with animations
Exporting and rendering
277
Rendering parameter files
You may sometimes wish to render all images and animations in a parameter file to disk. Instead of
rendering each image separately, you can render the entire parameter file to disk with one
command.
Hold down the Add button on the Render to Disk tool window, and click Add Parameter
File. Select a parameter file to render in the dialog box that appears, and click Open.
This will open the Render Parameter File to Disk dialog box. Here, you can specify a folder that will
contain the rendered bitmap images, the file format, the desired size and resolution, and the antialiasing settings.
You can choose to render all images in the parameter file, or only selected images, or only the
images that do not yet exist in the destination folder (useful to update a folder that holds the images
for a parameter file if you have added new parameter sets).
In addition, you can select if you only want to render the still images or the animations in the
parameter file, or both. For example, you can render the still images in PNG format and the
animations in AVI format by rendering the parameter file twice, selecting the Only Stills option the
first time, and Only Animations the second time, with appropriate file format settings.
Click OK to start rendering the parameter file. This will create a new render job that starts calculating
the images in the background. Render jobs can be monitored and managed in the Render to Disk
tool window.
Next: Render jobs
See Also
Exporting and rendering
Rendering images
Rendering animations
278
Render jobs
When you start rendering a fractal or a parameter file, a render job is created that performs the
requested calculations in the background. Render jobs are monitored and managed in the Render to
Disk tool window.
The tool window contains a list of render jobs. Below the list, the status of the selected job is shown,
including various statistics.
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Click the Pause/Start button to pause the selected job. To resume it, click the button again.
Click or hold down the Add button to add a new job. See Rendering images and Rendering
parameter files.
Click the Delete button to cancel and delete the selected job.
The icons before each job in the list show its type (single image or parameter file), and whether it is
currently calculating.
By default, only the job at the top is calculating. When it is finished, the next job in the queue is
started. New jobs are added at the bottom, and therefore will be started automatically when all the
other jobs have been completed.
To start another job, select a job in the list that is not calculating and click the Pause/Start button
to start it. When this job is finished, it will start the next job in the queue, too.
You can reorder the jobs in the queue by dragging them up or down to adjust the order in which they
will be calculated. For example, if you want a job to stay paused while the other jobs are calculated,
drag it to the top of the list, so it will not be started automatically.
Notes
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To get help on a specific statistic, hover the mouse cursor over it while the Fractal Mode tool
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window is open.
When you hide or close the tool window, the jobs will continue to calculate in the
background. When you close Ultra Fractal, the jobs will be paused. They will be resumed
automatically when you start Ultra Fractal again.
Although Ultra Fractal is carefully designed to resume jobs correctly in case of a power
failure or computer crash, you may want to back up time-consuming render jobs to be
absolutely safe. To back up a render job, right-click it in the list and click Backup Job. This
will save all calculated data to a single file (*.urj). To restore a job, hold down the Add
button and click Restore Job.
Next: Anti-aliasing
See Also
Exporting and rendering
280
Anti-aliasing
One of the reasons to render fractals to disk is to be able to use anti-aliasing. Anti-aliasing improves
the quality of rendered images by sharpening and smoothening them, removing jagged edges.
No anti-aliasing
Normal anti-aliasing
Anti-aliasing increases the time it takes to render the image. The effect of anti-aliasing and the extra
time required depends on the anti-aliasing settings you use when starting a render job (see
Rendering images and Rendering parameter files).
The following settings are available:
Anti-aliasing
Selects common anti-aliasing settings.
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●
●
●
●
Threshold
Off turns anti-aliasing off completely.
Quick selects minimal anti-aliasing settings that calculate relatively
quickly.
Normal selects normal anti-aliasing settings that provide good quality
and reasonable calculation times.
Non-adaptive turns off adaptive anti-aliasing. This gives better
results for some images, but it requires (much) longer to calculate.
Custom allows you to specify your own anti-aliasing settings.
Specifies the threshold to use for adaptive anti-aliasing. Ultra Fractal antialiases a pixel only when the difference between the pixel and its neighbors
(red + green + blue) is larger than or equal to the threshold.
Use 0 to turn adaptive anti-aliasing off. This slows the calculation down, but is
required if adaptive anti-aliasing does not work well (for example when the
fractal contains many thin lines, such as with the Embossed fractal formulas).
Depth
Specifies the anti-aliasing depth (1 or greater). Greater depths give better
quality at the expense of calculation time. Increasing the depth by one can
easily double or triple the calculation time. The default value of 1 is usually
sufficient.
Subdivisions
Selects how pixels are subdivided for anti-aliasing. The default value 9 (3x3)
gives better quality and is recommended. Use 4 (2x2) only for quick renders,
or when the depth is greater than 1.
The Normal setting is recommended, and will usually give the best results. If you are preparing
images for printing, it may not be necessary to use anti-aliasing. This is because on prints, individual
281
pixels are rarely visible due to the much higher resolution.
Next: File formats
See Also
Exporting and rendering
282
File formats
Ultra Fractal supports various image file formats for exporting and rendering images. You can select
the file format when selecting the file name of the exported image and when starting a new render
job (see Rendering images, Rendering animations, and Rendering parameter files).
The following file formats are supported:
Bitmap image
Saves the image as a Windows bitmap image (*.bmp). This format is
supported by almost all Windows graphics programs.
Photoshop image
Saves the image as an Adobe Photoshop image (*.psd). This allows you
to save layers individually, so they can be post-processed. This file
format also supports transparent images.
Note: Currently, layer groups are not preserved in the Photoshop file.
Instead, the fractal is exported as a linear list of layers, and any masks
attached to layer groups are applied to the last layer of the group. For
this reason, it is a good idea to turn group masks into normal layers
first, so you could re-apply them as mask later in Photoshop.
PNG image
Saves the image as a Portable Network Graphics image (*.png). This file
format is readable by many graphics programs and supports lossless
compression and transparent images.
JPEG image
Saves the image as a JPEG image (*.jpg). This format offers very good
compression. You can set the quality of the saved image to adjust the
file size. A value of 95% will usually give good results. Do not use this
format if you want the best possible image quality.
Targa image
Saves the image as a Targa image (*.tga). This is a common format for
high-end graphics programs, such as raytracers and 3D packages. It
supports transparent images.
TIFF image
Saves the image as a TIFF image (*.tif). This format is often used by
print shops and graphics designers working with Apple computers. It
also supports transparent images.
AVI movie
Only for animations. Saves the animation as a Windows AVI movie
(*.avi) with a selectable codec. Only codecs with a Video for Windows
interface are supported. DirectX-only codecs are not supported. If you
want the best quality, it is recommended to render animations to bitmap
sequences instead, and compress them later with third-party software
such as VirtualDub.
When you render an animation to a format other than AVI, it will be rendered as a sequence of
bitmap images.
Next: Resolution
283
See Also
Exporting and rendering
File types
284
Resolution
In Ultra Fractal, you can set a resolution value for your fractals in the Fractal Properties tool window,
and in the Render to Disk dialog. The resolution specifies the relation between the logical size of the
fractal in pixels, and its physical size in centimeters or inches. Normally, the resolution is set in DPI
(dots per inch), so the logical size and the physical size are related by this formula:
LogicalSize [Pixels] = PhysicalSize [Inches] * Resolution [DPI]
For example, a 1600x1200 fractal at 300 DPI is 5.33x4 inch or 13.5x10.2 cm. If you are going to
print your fractal, you probably know the resolution that your printer uses. If you type that in the
Render to Disk dialog, for example, you can directly set the size in centimeters or inches.
Ultra Fractal always uses pixels internally. It will just use the resolution value to convert physical
sizes to pixel values, and it will store the resolution value with the exported or rendered images.
Resolution values are not supported by the JPEG and Targa file formats.
It is important to realize that the only thing that really matters is the logical size in pixels. You can
always open a rendered image in Adobe Photoshop, for example, and change its resolution, which
will "magically" change the physical size as well. The ability to specify the resolution in Ultra Fractal
saves you from having to convert the desired physical size to a logical size in pixels yourself, but
remember that it is just a placeholder value.
See Also
Exporting and rendering
285
Network calculations
Note: You need Ultra Fractal Animation Edition for network calculations.
Ultra Fractal enables you to distribute calculations over multiple computers connected with a
network. This can greatly increase the speed at which complex fractals are calculated, especially in
combination with deep zooming.
Network calculations work by running a separate program called Ultra Fractal Server on remote
computers, and creating connections to those computers with the Network tool window in Ultra
Fractal. One server can accept multiple connections from different computers running Ultra Fractal,
and one computer running Ultra Fractal can create connections to multiple servers.
When you have successfully created one or more connections, calculations will immediately be
divided among all available computers. You can add or remove connections at any time. Both
calculations performed by fractal windows and calculations performed by render jobs can be
distributed.
Ultra Fractal uses the TCP/IP protocol for network calculations, so you can connect to computers both
on a local network and on the Internet.
Next: Network servers
See Also
Connections
Fractal windows
Exporting and rendering
286
Network servers
To be able to connect to a remote computer, the Ultra Fractal Server program must be running on
that computer. The server accepts connections from other computers running Ultra Fractal and
performs requested calculations.
To start the server, click Programs on the Start menu, and then click Ultra Fractal 5
Server. (The name can differ slightly depending on the version number.)
To run the server on another computer, you can install Ultra Fractal on that computer. Alternatively,
share the drive that Ultra Fractal is installed on (with Windows Explorer) so you can access it from
other computers, and then start the Server.exe program located on your own computer in the Ultra
Fractal folder from a remote computer.
The server shows a list with the current connections and a log that displays all activity. In the status
bar, the number of connections and the current IP address are shown.
By default, the server listens on port 8691 for connections, but you can change this if it causes
conflicts with other programs. If there is a firewall on the server computer, you need to configure it
to allow incoming connections on this port.
Click Options on the File menu of the server to set connection and security options for the
server. See Security.
Notes
●
●
●
If you want to keep the server running continously on a remote computer, create a shortcut
to it in the Startup folder in the Start menu. By minimizing the server window, it will run
unobtrusively in the taskbar tray area.
You do not need an extra license to run Ultra Fractal Server on other computers.
The computers that run Ultra Fractal Server do not require any fractal formulas, so you do
not need to have an updated collection of formulas on those computers.
Next: Connections
See Also
Network calculations
287
Connections
In the Network tool window, you can create and manage connections to other computers running
Ultra Fractal Server.
●
●
●
●
●
The Add Connection button creates a new connection. This will open a dialog box where
you can enter the address of the computer to connect to. To get help on a control in this
dialog box, click the ? button in the title bar, and then click the control.
The Delete Connection button deletes the selected connection.
The status icon before each connection shows its current status. Click on the icon to disable
and enable the connection.
In the list, the titles of the connections are displayed. Click on the title of the selected
connection to rename it. Double-click a connection to edit its properties. You can drag
connections up or down to organize them.
Below the list, various statistics on the selected connection are displayed.
Right-click inside the list to open a pop-up menu with frequently used commands.
Next: Tips
See Also
Network calculations
288
Tips
The following tips will help you to use network calculations effectively.
●
●
●
●
●
Network calculations work best with images that are slow to calculate. Especially deepzoomed fractals will benefit. If the fractal calculates relatively quickly, the network
communication overhead can sometimes outweigh the extra calculation speed.
Large images do not necessarily benefit more from network calculations than small images.
Connect to local computers rather than to computers on the Internet if you can help it,
because the communication overhead is likely to be much smaller on a local network (LAN).
On a LAN, use 100 Mbps or Gpbs Ethernet instead of 10 Mbps.
If you can, avoid using a personal firewall because it might make the network calculations
less efficient.
Try to connect to remote computers that are roughly as fast as your own computer. It does
not help much to connect to slower computers.
Next: Security
See Also
Network calculations
Network servers
289
Security
By default, a computer that runs Ultra Fractal Server accepts connections from any user on any
computer. However, you have several options to restrict access to the server.
Click Options on the File menu of the server, and then click the Security tab to set security
options.
●
●
You can restrict access to selected IP addresses or ranges of IP addresses. Using this
feature, you can for example only allow users on your local network to connect to the server.
You can require users to supply a password when creating a connection to the server. Users
without a valid password will not be able to create a connection. Passwords are transmitted
securely.
In the log at the bottom of the server window, you can see all connection activity. The log also shows
incoming connections that were not accepted because of a blocked IP address or an invalid
password. The log can also be written to a file so you can analyze it later.
See Also
Network calculations
Network servers
290
Writing formulas
In Ultra Fractal, every part of the fractal calculation process is controlled
by formulas. There are three types of formulas: fractal formulas,
coloring algorithms, and transformations. A formula can be seen as a
small, specialized computer program that is compiled and executed by
Ultra Fractal.
By writing your own formulas, you can completely customize how a
fractal is calculated. It is recommended to first learn how to use Ultra
Fractal and get comfortable with it before you start writing formulas.
This chapter explains how to write your own formulas. It is divided into five sections:
●
●
●
●
●
The Language basics section introduces the syntax and elements of the formula language.
You should study this first.
The Functions and classes section describes how to declare and use your own functions
and classes, including inheritance and class parameters.
The Formulas section shows how to use the formula language in practice to write fractal
formulas, coloring algorithms, and transformations.
The Reference section describes all operators, built-in functions, predefined symbols, etc.
that are available.
The Tips section contains additional information on debugging and publishing your formulas.
Use the Contents tab to navigate to topics in these sections.
Next: Creating a new formula
See Also
Fractal formulas
Coloring algorithms
Transformations
Copyright and tweaking
291
Creating a new formula
This topic shows step by step how to create your first fractal formula, a basic Mandelbrot set.
1. Create a new fractal. It does not matter which formula is selected, since it will be replaced by
your own.
2. Click New on the File menu, and then click Fractal Formula File. The formula editor
appears with an empty file.
3. Click New Formula on the Insert menu. Enter "My Mandelbrot" as the title and click OK.
The new entry should now appear in the formula editor.
4. After the init: label, insert the following line:
z = 0
This initializes the complex variable z to (0,0).
5. After the loop: label, insert the following line:
z = z * z + #pixel
This is the main equation for the Mandelbrot set. #pixel refers to the coordinates of the pixel
being computed and will be different for every pixel. The statements in the loop section will
be executed repeatedly.
6. After the bailout: label, insert the following line:
|z| < 4
This defines when Ultra Fractal should stop repeating (or iterating) the statements in the
loop section. With this condition, the loop section will be iterated as long as |z| (equal to
sqr(real(z)) + sqr(imag(z))) remains smaller than (4,0).
7. The formula should now look like this:
MyMandelbrot {
init:
z = 0
loop:
z = z * z + #pixel
bailout:
|z| < 4
default:
title = "My Mandelbrot"
}
8. Save the new formula by clicking Save As on the File menu. Enter "My Formulas.ufm" as
the filename and click Save.
9. Now, click the Browse button in the Formula tab of the Layer Properties tool window. Select
"My Mandelbrot" from the file "My Formulas" and click OK.
10. Congratulations! You have just created your first fractal formula.
Notes
●
●
If compiling the formula results in compiler errors, make sure you have entered the formula
correctly. Highlight the error in the Compiler Messages tool window and click the Trace
button to see where the first error occurred. Correct the error and click the Reload button in
the Formula tab to try again (changes in the formula will be saved automatically).
Try to experiment with the loop section. For example, change z * z into z * z * z and see
what happens. Click the Reload button in the Formula tab to reload the formula after you
have changed it.
292
Next: Formula files and entries
See Also
Fractal formulas
Formula editors
293
Formula files and entries
Formula files are plain text files with the extensions .ufm (fractal formula files), .ucl (coloring
algorithm files), or .uxf (transformation files). A formula file can contain any number of formulas
(called entries).
Each entry starts with an entry identifier, followed by the contents of the entry between curly
brackets { and }. After the entry identifier, an optional value between parentheses can be added.
Examples:
My-Formula {
; entry contents
}
Mandelbrot(XAXIS) {
; this formula uses an optional setting
}
comment {
The comment entry always consists of comments.
}
The entry identifier may consist of almost all characters, except spaces and tabs, of course. Since
you can specify an additional descriptive title for the formula, the identifier can be cryptic as the user
never notices it (but it is shown by the browser). The identifier is used to distinguish between
formulas in the same file, so no two formulas in the same file can have the same identifier.
The semicolon ; is used to add comments to a formula. After a semicolon, the rest of the line is
ignored by the compiler. You can also add global comments like copyright information to a file by
placing them inside a special comment { } entry, which is also ignored (but the browser shows it
when the file is selected).
To facilitate working with entries, the built-in formula editor can automatically create new entries and
search for existing entries. See Formula editors.
Next: Sections
See Also
Creating a new formula
Fractal formulas
Inheritance
294
Sections
Each entry in a formula file is divided into one or more sections. It depends on the formula type
which sections are supported and what they can contain. This topic describes sections in general. For
specific information about a formula type, see Transformations, Fractal formulas, and Coloring
algorithms.
Here is an example of a fractal formula:
MyMandelbrot {
init:
z = 0
loop:
z = sqr(z) + #pixel
bailout:
|z| < 4
default:
title = "My Mandelbrot"
}
This formula contains four sections. There are three types of sections:
●
●
●
Sections containing statements. These statements can be executed by Ultra Fractal; how and
when this happens depends on the particular section. Each statement must be on a separate
line, or they must be separated by commas. Examples of these sections are init and loop.
Sections containing a boolean expression. There's only one section of this type, the bailout
section.
Sections containing settings related to the formula. Settings always have the form "setting =
value". An example is the default section.
As you can see, sections are divided by labels. A label is just the name of the section followed by a
colon.
For compatibility reasons, it is sometimes allowed to omit the label in some sections. For more
information, see the formula-type specific documentation.
You can break long statements and settings across several lines using the backslash \ character. The
backslash character must be the last character on the line for this to work. Any spaces or tab
characters on the next line are removed, so if you want to add one or more spaces, you must put
them on the previous line (the line containing the backslash). Example:
default:
title = "A very long title \
for my \
favorite formula"
This is equal to:
295
default:
title = "A very long title for my favorite formula"
Next: Expressions
See Also
Formula files and entries
Global sections
Member visibility
296
Expressions
To recap briefly, a formula is divided into multiple sections, separated by labels. Some sections (for
example init and loop) can contain statements. Most statements are just expressions, and this topic
explains what expressions really are.
Almost everything is an expression. Variables, parameters and constants are all expressions. By
using operators or functions, expressions can be composed of one or two subexpressions. Examples:
a
3
3 + 2
sin(a)
(3 + sin(a)) / 2
These are all valid expressions (note that "a" is a variable). The important property of an expression
is that you can always calculate its value, no matter how complicated the expression is. Moreover,
you can do something with this value, for example assigning it to a variable by using the =
(assignment) operator:
b = 3 + 2
b = (3 + sin(a)) / 2
These expressions are called assignments. It is important to realize that assignments are expressions
themselves, so this is also a valid expression:
c = b = 3 + 2
This gives both c and b the value 5.
Now, remember that statements can be expressions, so that means any expression is a valid
statement. Of course, it does not make sense to use expressions like "3" or "(3 + sin(a)) / 2" as
statements, since nothing is done with the value of the expression, so the statement is ignored by
the compiler (and results in a warning message). Only assignments actually use the value of the
expression, therefore statements usually are assignments.
Note: do not confuse the = (assignment) operator with the == (equality) operator. The == operator
is used to test if two expressions are equal, and returns a boolean value (true or false).
Next: Types
See Also
Sections
Operators
Built-in functions
297
Types
To write formulas, you need to be aware of the concept of types. Expressions (constants, variables,
parameters, etc.) in formulas can have different types. There are five different built-in types. The
following table shows each built-in type and explains its use.
bool
Boolean expressions can only have two values: true or false. This type is
returned when expressions are compared:
3 < 4 ; true
false == true ; false
int
Integers are useful for counting. They can have values from -2147483648 to
2147483647. Most arithmetic operations can be performed on integers. Example:
3
-2
float
Floating-point numbers are the most familiar type of numbers. They can be very
small or large, and have virtually unlimited precision (see Arbitrary precision).
Their greatest benefit is that they can represent fractional values. Examples:
3.1
-2.9
1.3e7
complex
Complex expressions represent complex numbers. They consist of two floatingpoint numbers and are used to perform complex arithmetic, which is very useful
for fractal calculations. Examples:
(2.8, 4)
2.8 + 4i
color
Color expressions represent a color. You can perform operations on colors and
store them in color variables. Internally, a color is stored as four floating-point
values, corresponding to red, green, blue, and alpha (opacity) components. Each
value ranges from 0 to 1. Colors are intended only for direct coloring algorithms.
Note: You can add new types yourself by declaring classes. This is not necessary when you are
beginning to write formulas, though.
Next: Constants
See Also
Expressions
Type compatibility
Operators
298
Functions
299
Constants
Constants are used in formulas to specify fixed values. Example:
x = 3 * x + 4
Here, 3 and 4 are constants. This topic explains how constants are used in Ultra Fractal formulas,
and how Ultra Fractal determines the type of a constant (you should be aware of this).
Boolean constants are of type bool. There are only two boolean constants: true and false.
Integer constants are of type int. Integer constants are signed numbers within the range 2147483648 .. 2147483647. Examples:
5
-23
Floating-point constants are of type float. They consist of a signed mantissa, optionally followed
by the character E and a signed integer exponent to denote a power of ten. The exponent may range
from -4931 to 4931. Examples:
3.0
-1.23482
98.283E-3
-1e5
; 0.098283
; -100000
Complex constants are of type complex. They consist of two floating-point numbers, separated by
a comma and surrounded by parentheses. Alternatively, you can specify an imaginary number by
typing the letter i right behind a normal floating-point number. Examples:
(2, 3)
(3e2, 3.239)
2.3i
2 + 1.63i
; (300, 3.239)
; (0, 2.3)
; (2, 1.63)
Color constants are of type color. They are created by supplying the rgb, rgba, hsl, and hsla
functions with constant arguments. Examples:
rgb(0.5, 1, 0)
hsla(0, 0, 0.5, 0.5)
; orange
; transparent red
Next: Variables
300
See Also
Expressions
Types
301
Variables
Formulas are often composed of several separate calculations. Therefore, it is necessary to store
intermediate results in memory. To do this, you must use variables.
Identifiers are used to refer to variables. An identifier must start with a letter, followed by one or
more letters, digits or the underscore character "_". Here are some examples of valid identifiers:
x
MyOwnVariable
var_32
It does not matter if the letters are lower- or uppercase, so "myvar" and "MyVar" represent the same
variable. Some identifiers (called keywords) are reserved by the compiler for other purposes: you
cannot use them as variables.
Before you can read from a variable, you must first write to it. To do this, use the = (assignment)
operator:
x = 3
y = 3 + 28 / 7
The variable is created when it is first written to. By default, the type of the variable is complex, but
you can change that by placing a type keyword (bool, int, float, complex or color) in front of the
assignment. Alternatively, you can declare the variable before using it.
int i
i = 2
int x = 3
bool MyBooleanVariable = x > 3
Assignments are expressions themselves, so their result can be assigned again. This example gives
both x and y the value 1:
x = y = 1
To read from a variable, use the identifier in an expression. This example reads the value in x and
stores it in y:
y = x
Of course, you can also perform calculations when doing this:
302
y = x * 3 + 7
Next: Parameters
See Also
Arrays
Type compatibility
303
Parameters
Parameters are used to allow users to customize formulas without needing to rewrite them.
Parameters are used just like variables, with two exceptions: you cannot write to them, and you
must prefix them with the @ character (so the compiler can determine they are parameters instead
of variables). Here is an example that uses a parameter:
Mandelbrot {
init:
z = 0
loop:
z = z^@power + #pixel
bailout:
|z| < 4
}
The parameter used here is @power. In the Formula tab, the user can now enter a value for this
parameter and view the Mandelbrot set of any power using just one formula.
By default, the type of a parameter is complex. You can change that by adding a param block to the
default section of your formula and providing the necessary settings. Using the param block, you
can also specify enumerated parameters. With enumerated parameters, the user does not have to
enter a numerical value, but rather chooses an item from a drop-down list.
It is also possible to use user functions. These can be used just like normal functions, with the
exception that the user can choose the actual function from a list of all available built-in functions.
Here is an example with a user function:
Mandelbrot {
init:
z = 0
loop:
z = @myfunc(z) + #pixel
bailout:
|z| < 4
}
Now, the user can use sqr, but also sin and cos and many other functions with this formula. You
can customize the behavior of the user function using the func block in the default section.
Notes
●
●
It is possible to write to parameters, although this is not recommended and can make your
formulas run slower. It is provided for compatibility with old Fractint formulas.
There are six predefined parameters: p1..p6, and four predefined functions: fn1..fn4. You do
not need to use the @ prefix with these parameters and user functions. However, it is
recommended to use your own names instead of these (with the @ prefix) to make your
formulas easier to understand.
304
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●
●
●
The param and func blocks also provide settings for changing the caption, default, minimum
and maximum values of parameters and user functions, as well as adding a small help text.
Parameters are sorted alphabetically in the user interface, unless you provide a param block
for each parameter. In this case, the parameters appear in the order of the param blocks in
the formula file.
In the user interface, you can also group parameters together by adding headings.
For more information on using parameters with classes, see Class parameters.
Next: Arrays
See Also
Providing help and hints
Writing direct coloring algorithms
305
Arrays
Arrays are used to store multiple variables in an organized way. Before you can use an array, you
must declare it. Example:
int myArray[8]
This declares a static array called myArray with 8 elements. (It is called a static array because the
number of elements is fixed. To declare a dynamic array that allows the number of elements to be
changed later, see Dynamic arrays.)
You can use the elements in the array like normal variables:
myArray[0] = 1
myArray[myArray[0]] = 2 * myArray[0] + 1
You access an element in an array by specifying the index of the element between square brackets [
]. The index must be an integer expression, ranging from 0 to the number of elements - 1 (the value
0 corresponds to the first element in the array).
You can also declare and use multi-dimensional arrays by specifying multiple values between the
brackets. When declaring an array, the size of each dimension must be a constant integer
expression. Parameters and most predefined symbols also qualify as constants. Example:
float a[10, 2 * 6 - 2]
bool flags[#width, #height]
a[3, 5 - 3] = 1.5
flags[0, 0] = a[1 + 2, 2] > 0
You can directly assign arrays with the same size to one another:
color x[10]
color y[10]
x = y
Notes
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●
●
●
Unlike other types of variables, arrays are not initialized upon declaration. Be sure to
explicitly initialize all elements in arrays before reading from them. They will contain random
values otherwise. Reading from an array element that has not been initialized does not
generate a warning either, so you have to check your formulas carefully.
You will often use loops to iterate through the elements of an array.
Arrays are often filled with pre-calculated values in the global section to speed up
calculations.
If you use constant array indices outside the supported bounds, the compiler will produce an
306
●
error message. If you use expressions that evaluate to an invalid index value while the
formula is executed, a run-time message is written to the Compiler Messages tool window if
the debug compiler directive is defined. See Compiler directives.
If you assign arrays to one another that are incompatible and the size of the arrays is
unknown at compile time, a run-time message occurs, too.
Next: Dynamic arrays
See Also
Types
Variables
307
Dynamic arrays
In addition to static arrays, you can also declare dynamic arrays. Unlike static arrays, which have a
predetermined number of elements, the number of elements in a dynamic array can be changed at
any time. Example:
int anotherArray[]
This declares a dynamic array called anotherArray. Before you can store anything in this array, you
need to call the setLength function to set the number of elements that it can contain:
setLength(anotherArray, 12)
You can now use the elements in the dynamic array:
anotherArray[0] = 8
anotherArray[1] = anotherArray[0] * 2
Like static arrays, the index of the element can range from 0 to the number of elements - 1. The
index value 0 corresponds to the first element in the array.
At any time, you can call setLength again to resize the array. The length function always returns the
current size of the array:
setLength(anotherArray, 20)
int currentSize = length(anotherArray)
; returns 20
Unlike static arrays, dynamic arrays cannot be multi-dimensional. If you need a multi-dimensional
array, you can simulate it like this:
; Simulate a 10x10 two-dimensional array
int twoDimArray[]
setLength(twoDimArray, 10 * 10)
; Initialize the element at position [0, 0]
twoDimArray[0 * 10 + 0] = 13
; Initialize the element at position [8, 2]
twoDimArray[8 * 10 + 2] = 14
Also unlike static arrays, it is not possible to copy dynamic arrays with a single assignment. This will
compile, but result in the Arrays are not compatible run-time error message:
int a[]
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int b[]
setLength(a, 10)
setLength(b, 10)
a = b
; Generates run-time error message
Use a loop to copy the individual elements instead.
Notes
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●
●
Unlike static arrays, the elements of a dynamic array are zero-initialized by the setLength
function.
As with static arrays, if you try to access elements of the array that are out of range, a runtime error message will be written to the Compiler Messages tool window if the debug
compiler directive is defined.
Dynamic arrays are slightly less efficient than static arrays, so use a static array if possible.
Next: Type compatibility
See Also
Arrays
Types
309
Type compatibility
As explained in Types, every expression has a type. If an expression is a variable, a constant or a
parameter, its type is equal to the type of the variable, constant or parameter, of course. This topic
explains what happens if an expression is composed of two subexpressions with different types.
Consider this example:
3 + 2.1
The type of "3" is int, and the type of "2.1" is float. The type of the resulting expression is always the
"highest" type of the subexpressions. High means "most descriptive" here. For example, complex is
higher than float, which is in turn higher than int (boolean expressions are treated differently). So,
this means the type of the expression above must be float. Since its result should be 5.1, this
behaves as you would expect.
This means, however, that "3", a constant of type int, must be converted to "3.0", a constant of type
float. This conversion is performed automatically by the compiler. You should be aware of the fact
that the compiler can only convert types to higher types. For example, it cannot convert a float to an
int. So this statement is illegal and results in an error message:
int i = 3.1
Functions like round and real are available to perform these conversions manually, if this is
necessary.
Be aware of the fact that some operators and most functions always return float or complex values.
For example, this statement is illegal, since the division operator / cannot return an integer result (it
returns 1.5):
int i = 3 / 2
You can look up the behavior of all operators and functions in the Reference section.
The compiler can convert booleans to other types and vice versa, but it does generate a warning for
each conversion. The value true is converted to 1, and the value false to 0. An expression of
another type (int, float or complex) is converted to false if it is equal to 0, otherwise it is converted
to true. Please note that this is only supported for compatibility with old Fractint formulas. It is not
recommended to use this in new formulas.
Colors cannot be converted automatically. Use the rgb, rgba, hsl, and hsla functions to convert
floating-point values to colors. Use red, green, blue, hue, sat, lum, and alpha to convert colors to
floating-point values.
For the type compatibility rules for classes, see Inheritance and Casting.
Next: Conditionals
310
See Also
Expressions
Variables
311
Conditionals
This topic describes the if statement. The if statement is used to write pieces of code that should
only be executed under certain circumstances (conditions). Here is an example:
if a > 3
b = 2
else
b = 1
a = 2
endif
In this code snippet, b is given the value 2 when a is greater than 3, otherwise b is given the value
1, and a is given the value 2.
Here is the complete syntax of the if statement:
if <boolean-expression>
<statements>
[elseif <boolean-expression>
<statements>]
[else
<statements>]
endif
The parts between brackets [ ] are optional. There can be as many elseif blocks as you find useful.
Here is an example which finds the largest of three variables a, b and c and places it in x:
if a > b && a > c
x = a
elseif b > c
x = b
else
x = c
endif
The usage of elseif is not really necessary. The following example does exactly the same thing:
if a > b && a > c
x = a
else
if b > c
x = b
312
else
x = c
endif
endif
This example uses a nested if statement (an if statement within another if statement). If
statements may be nested as much as you want.
When evaluating the boolean operators && and ||, Ultra Fractal uses short circuit evaluation. The
expression is evaluated from left to right and Ultra Fractal stops as soon as the answer is known.
This is more efficient and it allows you to write expressions like these:
int i = -1
float a[10]
if i >= 0 && a[i] > 2
...
endif
In this case, Ultra Fractal detects that i is negative, so it will never even try to read a[i], which is
exactly what we intend because -1 would not be a legal index value for the array.
Notes
●
●
In Fractint, it is necessary to surround the boolean expressions after if and elseif with
parentheses. Ultra Fractal does not require this, but it is not harmful.
For more information on boolean operators like &&, see Operators in the Reference section.
Next: Loops
See Also
Expressions
Types
313
Loops
Sometimes you may want to repeat a sequence of statements. Ultra Fractal provides two constructs
to do this: the while loop and the repeat loop. Here is the syntax:
while <boolean-expression>
<statements>
endwhile
repeat
<statements>
until <boolean-expression>
The while loop repeats the statements as long as the boolean expression is true. If the boolean
expression is or becomes false, the statements are never or no longer executed. The repeat loop,
however, repeats the statements until the boolean expression becomes true. This means that the
statements are always executed at least once.
If you want the statements to be executed at least once, use the repeat loop. Otherwise, use the
while loop.
Here is an example that calculates x = n! (defined as x = 1*2*3*...*(n-2)*(n-1)*n), first using a
while loop, and then using a repeat loop:
int n = 23
; or another value
float x = 1 ; float because 23! is very large
while (n > 1)
x = x * n
n = n - 1
endwhile
int n = 23
float x = 1
if n > 1
repeat
x = x * n
n = n - 1
until n == 1
endif
Obviously, the while loop is better suited to calculate the factorial of a number, but in other cases
the repeat loop may be better.
As with if statements, loops may be nested as much as you want.
314
Next: Functions
See Also
Conditionals
Arrays
315
Functions
As you write larger formulas, it becomes desirable to avoid code duplication and to have a way to
better structure the formula code. To do this, you can group code in functions that you can call just
like the built-in functions.
Here is a complete Mandelbrot formula that shows how to declare and use a function that calculates
one iteration of the Mandelbrot set:
MandelbrotWithFunction {
init:
complex func calculateMandelbrot(const complex x)
return sqr(x) + #pixel
endfunc
z = 0
loop:
z = calculateMandelbrot(z)
bailout:
|z| < 4
}
●
●
●
●
●
●
●
Functions start with the func keyword and end with the endfunc keyword. (These keywords
are also used for function blocks.)
The return type of the function is specified before the func keyword. For a function with no
return value, leave out the type before the func keyword.
Arguments to the function are declared after the name of the function between parentheses.
See Function arguments for more information.
A function needs to return its value with the return keyword. The return keyword causes an
immediate exit of the function with the specified return value. It is required in functions with
a return value. In functions without a return value (also called void functions or procedures
in other languages), you can use return to exit the function prematurely, but it is not
required. See Function arguments for an example.
Functions can declare local variables, but they can also access the variables from the formula
in which they are declared.
Functions declared in a formula can only be accessed by the formula itself. If you want to
access a function from another formula, declare it as a static class method instead.
Function declarations can occur anywhere in a formula where you can write "normal" formula
code. The order in which functions are declared does not matter: it is legal to call a function
that is declared later in the formula. A function can also call itself recursively.
Functions declared in a global section can write to global variables, but you cannot call these from
outside the global section, unless the entire function is declared as const (in which case it can only
read from any variables):
Test {
global:
float x
float func getXSquared() const
316
return x * x
endfunc
init:
z = getXSquared()
...
}
Next: Function arguments
See Also
Built-in functions
Methods
317
Function arguments
Most function declarations include one or more function arguments. Function arguments are declared after the
name of the function between parentheses.
●
●
●
●
Each argument declaration contains the type and the name of the argument. Within the formula, the
argument can be used just like a normal variable. Function arguments can be of type bool, int, float,
complex, color and object. You cannot pass an entire array as a function argument, but you can of course
pass individual array elements. To pass an entire array, wrap it in an object (see the array wrapper
classes in common.ulb).
Optionally, the const keyword can be put before the type of the argument. This tells the compiler that the
function will not change the value of the argument, which can make calling the function more efficient
(currently this matters only for float, complex, and color arguments).
Sometimes, a function needs more than one return value. In this case, you can declare a by-reference
argument with a & symbol before the name. Such an argument is passed by reference, instead of by
value, which enables the function to write a value back to it that the caller will receive.
Objects are always passed by reference, so it is almost never needed to use the & symbol with object
arguments. You should use it only in case you want a function to be able to actually change the object
variable owned by the caller.
Examples:
complex func square(const complex x)
; Squares x and returns the result.
return x * x
endfunc
func square2(complex &x)
; Squares x and returns the result in x.
x = x * x
endfunc
bool func isPowerOfTwo(int value, int &powerOfTwo)
; Checks if value is a power of 2, such as 32 or 64. If so, returns true
; and returns the power of two in powerOfTwo. Otherwise returns false.
powerOfTwo = 0
if value > 0
int mask = 1
int i = 0
while i < 31
if value == mask
powerOfTwo = i
return true
endif
mask = mask * 2
i = i + 1
endwhile
endif
return false
endfunc
; Examples of how to call these functions:
complex c = (2, 0)
c = square(c) ; c = (4, 0)
318
square2(c)
; c = (16, 0)
int pow
if isPowerOfTwo(64, pow)
; pow = 6 here, because 2^6 = 64.
...
endif
Next: Classes
See Also
Built-in functions
Methods
319
Classes
While function declarations in formulas are useful, you cannot access them from another formula. To
be able to re-use code in multiple formulas, you need to use classes instead.
●
●
●
●
A class is a declaration of a set of variables and functions that operate on these variables.
An object is an instance of its class. This class is the type of the object, just like int is the
type of an integer variable.
The variables of a class are called fields.
The functions of a class are called methods. Both fields and methods are also known as the
members of a class.
Classes are declared in formula files, or in class library files with the .ulb file extension. A class looks
a bit like a regular formula entry, but the entry identifier is preceded by the class keyword. Here is
an example of a simple class that represents a point with integer coordinates:
class Point {
public:
func Point(int aX, int aY)
x = aX
y = aY
endfunc
float func distance(Point p)
; Returns the distance to the second point p.
return sqrt(sqr(p.x - x) + sqr(p.y - y))
endfunc
int x
int y
}
This class, named Point, contains a constructor, which is a special function that initializes an instance
of the class. The constructor always has the same name as the class. Also, there is an additional
method called distance, and two fields called x and y that store the coordinates of the point.
Next: Objects
See Also
Inheritance
Class parameters
320
Objects
To use a class, you have to create instances of the class, which are called objects. In Ultra Fractal,
you always use a reference to the object. Such an object reference can be stored in a variable with
the class name as type.
Let's create some objects using the example Point class given in Classes:
; Declare a new object variable
Point p
; Create a new Point object and store it in p.
p = new Point(3, 4)
float d = p.distance(new Point(0, 0)) ; Returns 5
The new operator takes the name of the class as a function, together with the arguments for the
constructor. It creates a new instance of the Point class and returns a reference to it.
When you copy an object variable, you only copy the reference to the object, not the object itself.
Copying an object variable therefore does not create a new object. Example:
Point pt1 = new Point(3, 4)
Point pt2 = pt1 ; This copies a reference!
pt2.x = 10
; Now pt1.x is also 10
print(pt1.x)
; This will print 10
pt2 = new Point(pt1.x, pt1.y) ; Creates a true copy
pt2.x = 6
; Only modifies the copy
print(pt1.x)
; This still prints 10
print(pt2.x)
; This prints 6
You can also set an object variable to the special value 0, the null reference. This clears the
reference, so it points to no object at all. This is often useful when programming, for example when
building a linked list. You can test if an object value is empty by comparing with 0, or by treating it
as a boolean expression:
Point p = 0
if p != 0
; This will not be executed.
endif
if p
; Will not be executed, same as above.
endif
int x = p.x ; Compiles, but illegal!
if p
321
x = p.x
endif
; This is safe
When an object reference can be null, as in the example above, you need to test it first. Only use the
object reference if it is non-null. If you access a field or method using a null object reference, Ultra
Fractal will generate a run-time error and halt execution of the current calculation.
Next: Member visibility
See Also
Classes
Memory management
322
Member visibility
Like formulas, class declarations are divided in three sections, called public, protected, and private (in this
order). Each section can contain member declarations: fields and methods. The type of section determines the
visibility of the members that it contains.
●
●
●
Members in the public section are accessible to formulas and other classes. This is the public interface of
the class: the part that is intended to be visible to the outside world.
Members in the protected section are accessible only to derived classes. This is often useful to change
the inherited behavior of a class in a descendant. See Inheritance.
Members in the private section can only be accessed by methods from the same class. Formulas or other
classes cannot access them. This is useful for storing the internal data for the class, because you are sure
that no other class can interfere with it.
Generally, the public section contains the constructor for the class, and the methods that make up its public
interface. All fields and internal methods should go into the private section. If it is necessary to access a field from
outside the class, the best design is to create a method to access it (commonly called a getter or setter). This
allows you to change the internal representation of the class later, while keeping the public interface the same.
If you do not specify a section, it is assumed to be public. Many examples in this help file use this for brevity, but
for real classes, it is recommended to define the visibility explicitly.
Here is an example of a simple Texture class that can distort a complex value:
class Texture {
public:
func Texture()
fAmount = 0.1
fSeed = 1234
endfunc
complex func distort(const complex x)
; Adds a small random value to x and returns the result.
return real(x) + getRandomValue() + flip(imag(x) + getRandomValue())
endfunc
float func getAmount()
; Returns the amount of distortion.
return fAmount
endfunc
func setAmount(const float amount)
; Sets the amount of distortion
fAmount = amount
endfunc
private:
float fAmount
int fSeed
float func getRandomValue()
; Return a new random value using the current seed.
fSeed = random(fSeed)
return fAmount * (fSeed / #randomrange)
323
endfunc
}
All fields in this class are private, and the amount of distortion can be accessed with getAmount and setAmount.
The getRandomValue method is private because it is only used within the class.
For completeness, here is how you would use this class:
Texture tx = new Texture
print(tx.distort((2, 3)))
print(tx.distort((2, 3)))
; Prints (1.968, 2.945)
; Prints (2.001, 3.062)
Note: classes can also have a default section for specifying the title and parameters of the class. See Class
parameters.
Next: Inheritance
See Also
Classes
Fields
Methods
324
Inheritance
Class inheritance enables you to create a new class that derives from an existing class. The derived
class is called a descendant; the class it derives from is called the ancestor or base class. A
descendant inherits all fields and methods from the ancestor and can add new fields and methods.
Also, the descendant can change the behavior of the ancestor by overriding one or more methods.
To derive from a class, specify its name within parentheses after the name of the class. Example:
class Base {
int x
int func getXPlusOne()
return x + 1
endfunc
}
class Derived(Base) {
int y
int func getXPlusY()
return x + y
endfunc
}
The Derived class contains both the members from itself, and the members from Base. Let's test
this:
Derived d = new Derived
d.x = 2
d.y = 3
print(d.getXPlusOne()) ; Prints 3
print(d.getXPlusY())
; Prints 5
You can assign a derived object to a variable that has the type of the ancestor class, because a
derived object is always compatible with its ancestor:
Derived d = new Derived
d.x = 4
d.y = 5
Base b = d
print(b.x) ; Prints 4
print(b.y) ; Compilation error!
●
Use inheritance sparingly. Inheritance is only suitable if the descendant class has an "is-a"
relationship with the ancestor. For example, you should never derive a Rect class
325
●
●
●
●
●
(representing a rectangle) from a Point class, because a rectangle is not a point. You could
however derive a Car class from a Vehicle ancestor, because a car is a type of vehicle. If
there is not an "is-a" relationship, use the other class as a field. For example, a Rect class
could have two fields of type Point: leftTop and bottomRight.
In Ultra Fractal, inheritance is primarily useful in combination with class parameters.
You can include a file name with the ancestor if it is declared in another file. See Importing
classes.
The chain of classes that is built with inheritance is called a class hierarchy.
If no ancestor is specified, the class descends from the internal Object base class. This
means that all classes ultimately have Object as a common ancestor. See also Casting.
See Overriding for more information about overriding methods and changing the behavior of
a descendant class.
Next: Fields
See Also
Classes
Casting
326
Fields
Member variables in classes are called fields. Fields are used to store the internal data for a class.
●
●
●
●
It is recommended to always declare all fields in the private section of a class, unless the
class is very simple and mainly used to group a set of variables. As an illustration, compare
the Point example with the Texture example.
By convention, field names start with a lowercase "f", such as fMyData. This allows you to
easily see the difference between fields and local variables or arguments.
Fields can be of any type, just like variables. They can be arrays, dynamic arrays, or object
references. The type of a field can even be the type of the class that it is declared in, so you
can create recursive data structures like a tree or a linked list.
Unlike formula variables or local function variables, all fields of a class are automatically
initialized to 0. Use a constructor to initialize them explicitly.
Here is a very simple example of a linked list node that refers to itself:
class Node {
Node next
int data
}
Usage example:
Node head = new Node
head.data = 2
head.next = new Node
head.next.data = 3
Node n = head
while n
print(n.data) ; Prints 2 and 3
n = n.next
endwhile
Note that it is not necessary to initialize the next reference when creating a node, because it is
automatically initialized to 0, the null reference.
Next: Methods
See Also
Classes
Variables
327
Methods
Member functions in classes are called methods. Methods typically perform operations on the fields
of a class. Methods are declared just like functions in a formula.
Methods always operate on an instance of the class (except static methods). The instance is returned
by the reserved this reference. Here is an example:
class Data {
int x
func printMe(Printer p)
p.printData(this)
endfunc
}
class Printer {
$define debug
func printData(Data d)
print(d.x)
endfunc
}
If you call a method on an object reference, the this reference inside the method will return the
object reference that it was called on.
Data d = new Data
d.x = 12
d.printMe(new Printer)
; Prints 12
In this code fragment, the this reference in Data.printMe() will return the d reference, which is then
passed to the Printer object.
Note that objects are always passed to functions and methods by reference (see also Function
arguments). For example, the Printer.printData() method could change the x value of the Data
object that it receives. If you include the & symbol with the function argument (as you would do for
normal by-reference argument passing), this lets the function modify the actual object reference
which is often not needed.
Next: Overriding
See Also
Classes
Fields
Static methods
328
Overriding
In a derived class, you can override inherited methods to change their behavior. When overriding a
method, the declaration must match exactly, including the argument names and types and the
return type. (Ultra Fractal supports covariant return types, so if the return type is a class, it can also
be a descendant of the return type of the inherited method.)
In the overridden method, you can call the inherited method using the ancestor class name and the
member operator. Here is an example where the Derived class overrides a method inherited from
Base, and calls the inherited method:
class Base {
int func test()
return 3
endfunc
}
class Derived(Base) {
int func test()
return Base.test() * 2
endfunc
}
Ultra Fractal always uses virtual method dispatching for all methods. This means that when you call
a method on an object, the actual type of the object is determined and the method for that object
type is called. This matters when using inheritance and method overriding:
Base b = new Base
print(b.test()) ; Prints 3
Derived d = new Derived
print(d.test()) ; Prints 6
; Test virtual method dispatching
Base x = b
print(x.test()) ; Prints 3
x = d
print(x.test()) ; Prints 6
When x.test() is executed, the actual type of x is determined and the corresponding method is
called. In the first case, the actual type of x is Base, so Base.test() is called, which returns 3. In the
second case, Derived.test() is called because the actual type of x is Derived, even though x is
declared as a reference to Base. This behavior is extremely useful with class parameters.
Note: Unlike methods, member variables are never overridden. If you declare a variable in a derived
class with the same name as a variable in the ancestor class, the new variable will exist in addition to
the (now hidden) inherited variable. Because the new variable doesn't have any relationship with the
inherited variable, it is legal for it to be of a different type. Generally, declaring variables with the
same name as inherited variables is not recommended since it can easily lead to confusion.
329
Next: Constructors
See Also
Classes
Inheritance
Methods
330
Constructors
As briefly explained in Classes, a class can contain a constructor. A constructor is a special method
that is called automatically by the new operator when an instance of the class is created. The task of
the constructor is to initialize the fields of the just created object.
The constructor has the form of a method without a return type, and its name must be equal to the
name of the class. Optionally, the constructor can have one or more arguments, which must be
passed when creating an object of the class. This makes it possible to immediately initialize the
object to the desired state.
class Test {
func Test(int arg)
x = arg
endfunc
int x
int y
}
Before the constructor is called, all fields of the class are initialized to 0. You only need to initialize
those fields that must have a different initial value.
Test t = new Test(3)
print(t.x) ; Prints 3
print(t.y) ; Prints 0
When using inheritance, the constructor of the derived class must have the same arguments as the
ancestor class. (This is required because the constructor is also a virtual method.)
The constructor of the derived class can call the inherited constructor by using the name of the
ancestor as a function. Calling the inherited constructor is almost always necessary because
otherwise the ancestor will not be initialized correctly. Example:
class Derived(Test) {
func Derived(int arg)
Test(4) ; Call the inherited constructor
w = arg
endfunc
int w
}
Derived d = new Derived(7)
print(d.x) ; Prints 4
print(d.w) ; Prints 7
331
You can also call a constructor on an already constructed object, in which case it will execute as a
normal function. This might be useful to reset the object.
Next: Static methods
See Also
Classes
Inheritance
Methods
332
Static methods
Normal methods in a class always operate on an instance of that class, so they need to be called on
an object reference. In the method, the object reference that it was called on is returned by the this
keyword.
Static methods, in contrast, do not operate on an instance of the class. They can only perform
operations on the function arguments and on local variables. Therefore, you can use static methods
as global functions, except that they are grouped by the class that contains them.
You declare a static function with the static keyword, which must appear just before the function
declaration. Example:
class Utils {
static int func min(int a, int b)
if a < b
return a
else
return b
endif
endfunc
}
You can call a static method with the class name, or with an object reference (an instance of the
class) and the member operator:
; Call with class name (preferred)
print(Utils.min(3, 5)) ; Prints 3
; Call with object instance
Utils u = new Utils
print(u.min(3, 5))
; Prints 3
Calling a static method is slightly more efficient than calling a normal method.
Next: Casting
See Also
Classes
Variables
333
Casting
When you assign an object reference to a variable, or pass it to a function, the type of the reference
and the expected type should be compatible. As explained in Inheritance, a derived object is always
compatible with its ancestor. Let's try this:
class
int
}
class
int
}
Base {
x
Derived(Base) {
y
Derived d = new
Base b = d
b.x = 4
print(d.x)
Derived d2 = b
Derived
; Legal because Base is ancestor of Derived
; Prints 4
; Compilation error: incompatible types!
The last assignment is illegal because b has type Base, which is not compatible with Derived.
However, b really points to an object of type Derived, so it should be possible to get the 'original'
object back. You can do this with a cast. A cast looks like a function call, using the name of the class
to cast to as the name of the function:
Derived d = new Derived
d.y = 5
Base b = d
Derived d2 = Derived(b)
print(d2.y)
Base b2 = new Base
d2 = Derived(b2)
print(d2)
; Cast b to Derived
; Prints 5
; This cast fails and returns 0
; Prints 0
A cast checks if the object is really an instance of the class to cast to. If so, it returns a reference
with the desired type. Otherwise, it returns a null reference. You can use this to query the type of
object that a reference actually points to.
Because all classes ultimately descend from the internal Object class, you can use Object as a
common type to store different types of objects in an array, for example. With a cast, you can later
test what type of object an element in the array really contains.
For debugging purposes, you can also print the value of an object reference, which will print the
class name and the reference count of the object:
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Object obj = new Derived
print(obj) ; Prints Derived (1)
Note: With a class parameter, you can also determine the currently selected class by comparing it
to a class with the == operator or the != operator. See Extending class parameters.
Next: Class parameters
See Also
Classes
Inheritance
335
Class parameters
Like formulas, classes can also have parameters and a title, which are declared in the default
section. This matters only if the class is in turn declared as a class parameter for a formula. In this
case, the class appears in the list of parameters in the Layer Properties tool window, with the
parameters for the class grouped with the title of the class. (See Example 1 - Formula classes for a
screen shot.)
Here is a simple example of a class that implements a simple bailout condition for a Mandelbrot-like
fractal formula. The bailout value is exposed as a parameter.
class Bailout {
public:
func Bailout()
; Empty constructor, see Extending class parameters
endfunc
bool func hasBailedOut(const complex z)
return |z| > @bailout
endfunc
default:
title = "Simple Bailout"
float param bailout
caption = "Bailout value"
default = 4
min = 1
endparam
}
To use this class and include its parameters in the parameter list for a formula, declare a class
parameter in the formula. A class parameter is declared by a parameter block with the name of the
class as its type.
MandelbrotTest {
init:
z = (0, 0)
Bailout bo = new @bailoutParam
loop:
z = sqr(z) + #pixel
bailout:
!bo.hasBailedOut(z)
default:
Bailout param bailoutParam
caption = "Bailout Test"
endparam
}
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Notes
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Normally, you create an instance of a class with parameters using new and the class name.
In this case, all parameters always remain at the default value. The class parameter
bailoutParam in the MandelbrotTest formula represents a variant of the Bailout class that has
different parameter values, set by the user. To create an object that uses these user-set
parameter values, use the new operator with the class parameter as shown above.
You can create more than one object from a single class parameter, and you can have
multiple class parameters of the same class type, which have their own independent set of
parameters.
Inside a class, all parameters must be declared by a parameter block. (In contrast, formulas
can have undeclared parameters for Fractint compatibility.)
Optionally, a class can also contain a rating setting in its default section.
Next: Extending class parameters
See Also
Classes
Parameter blocks
Function blocks
Headings
337
Extending class parameters
Class parameters make it easy to create different formulas with common features, but you can even
take this a step further. If you load the MandelbrotTest example in Ultra Fractal, a Browse button is
visible next to the name of the class in the list of parameters. This button enables the user to select
a different class than the default Bailout class, as long as it descends from Bailout. (See Example 1 Formula classes for an example.)
Let's write a descendant class that implements more bailout options:
class ExtendedBailout(Test.ufm:Bailout) {
public:
bool func hasBailedOut(const complex z)
return (@test == "mod" && |z| > @bailout) ||
\
(@test == "real" && sqr(real(z)) > @bailout) || \
(@test == "imag" && sqr(imag(z)) > @bailout)
endfunc
default:
title = "Extended Bailout"
int param test
caption = "Bailout Test"
default = 0
enum = "mod" "real" "imag"
endparam
}
If you put this code in a class library file such as Test.ulb, you can select the new class by clicking on
the Browse button next to the Bailout class parameter. The MandelbrotTest formula will now use the
bailout code from the ExtendedBailout class. As you can see, this system enables you to add new
features to a formula even after it has been published, without having to modify the formula itself!
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The descendant class must be declared in a class library file with the .ulb file extension so
the browser can find it. Therefore, the file name of the ancestor needs to be specified as
well. The example code above assumes that both MandelbrotTest and the Bailout class are
declared in a file called Test.ufm. See also Importing classes.
The ExtendedBailout class overrides the hasBailedOut method to change its behavior. Note
that it introduces a new parameter called test. The bailout parameter is inherited from the
Bailout base class.
If you want the class to appear in the browser when selecting a value for the class
parameter, make sure it has a title. Classes without a title are not visible in the browser.
(This is useful for abstract base classes, as explained in the next paragraph.)
In this example, the Bailout base class already has a default behavior and a parameter. In
practice, it might be better to have an abstract base class that only declares the methods
that form the public interface for the class. Do not include a title for the abstract base class
(the browser will only show classes that have a title). In the class parameter declaration for
the formula that uses an abstract class, you can then use the default setting to select a
descendant of the base class that is declared in a corresponding class library file. In this way,
the abstract base class is never used on its own, just as a base class.
A descendant can also override parameters from its ancestor by including a parameter
block for an inherited parameter. This parameter block completely replaces all previous
338
●
●
●
settings for the parameter. With this, you can for example change the default value of a
parameter, or hide it by setting visible to false. The type of the parameter must remain the
same.
In case you do not want to provide the option to the user to select a descendant class for a
class parameter, set the selectable setting of the class parameter to false.
The base class must have a constructor (possibly empty), otherwise the constructor of the
descendant class will never be called. The compiler will generate a warning if you use a base
class without a constructor for a class parameter, and the selectable setting is not false.
You can determine the currently selected class of a class parameter by comparing the class
parameter to the class directly with the == operator or != operator. This allows you to show
or enable other parameters depending on the currently selected class. (You can also
determine the selected class with a cast, but that requires the creation of an object of the
class, something you cannot do in visible or enabled settings.)
Next: Parameter forwards
See Also
Classes
Class parameters
Inheritance
Overriding
339
Parameter forwards
When you rewrite an existing formula to take advantage of class parameters, this changes the
format of parameter sets that are saved while this formula is in use. This means that existing
parameter sets cannot be opened anymore. To solve this problem, use parameter forwards.
A parameter forward declares a new parameter name in the formula, and lets it point to a subparameter of a class parameter. For example, suppose that an earlier version of the MandelbrotTest
example handled its bailout condition itself, with a float parameter named bailout. Now, however, the
equivalent parameter is bailout from the bailoutParam class parameter. The following parameter
forward expresses this:
MandelbrotTest {
; ...
default:
Bailout param bailoutParam
caption = "Bailout Test"
endparam
param bailout = bailoutParam.bailout
}
A parameter forward starts with the param keyword, the name of the old parameter, the = symbol,
and then the "path" to the new parameter, which contains parameter identifiers separated by dots.
In this case, when Ultra Fractal loads an old parameter set, the parameter set will contain the value
for a parameter named bailout. Because the formula does not contain a parameter named bailout,
Ultra Fractal will search its parameter forwards and will subsequently set the bailout parameter of
the class that is the default class for the bailoutParam class parameter (in this case the Bailout
class).
For this to work correctly, obviously the default class for the class parameter must be compatible
with the previous behavior of the formula. (You can set a default class with the default setting.) This
is your responsibility as formula author.
Next: Importing classes
See Also
Classes
Class parameters
340
Importing classes
When a formula or a class contains a class name, for example to declare a variable or a class
parameter, Ultra Fractal searches for the class in the list of imported files, and then in the current
file. To import a file so its classes become available, use the import keyword.
class ExtendedBailout(Test.ufm:Bailout) {
public:
import "common.ulb"
; ...
}
This modified version of the ExtendedBailout example first imports the file Test.ufm because that is
where its ancestor is located. Then it imports the class library file common.ulb.
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●
●
The import keyword expects a file name within double quotes, without any path
information. The file is located using the current formula search paths as set in the Folder
tab of the Options dialog.
If a file name is specified in the ancestor specification of a class, this behaves as if this file
was imported before any other files. The browser, however, needs the specification of the
ancestor file name here to be able to check the inheritance of classes when you select
another class for a class parameter.
The order in which import statements occur is important. When searching for a class, Ultra
Fractal searches the file that was last imported first, and so on. Other than that, import
statements can occur anywhere in a formula or class. Even the statements before an import
statement are affected by it, because import statements are read and applied before the rest
of the code is checked for consistency and type compatibility. Therefore it is recommended
to put your import statements at the top of a formula or class.
Class library files with the .ulb extension have two purposes. When looking for classes for
class parameters, the browser will only look in .ulb files. So any derived classes intended to
extend class parameters must be in a class library file. Also, class library files provide a
logical place to put classes that are intended to be shared by different fractal formulas,
coloring algorithms, and transformations.
The common.ulb file that is installed with Ultra Fractal provides many useful base classes.
See The common.ulb file.
You can also import classes from .ufm, .ucl, or .uxf files if you have to, but this is
recommended only for files that you control yourself. If you are a formula author and you
want to provide common functionality to other authors, put them in your own .ulb file. Do
not import a class from another author's .ufm/.ucl/.uxf file because it might be changed in a
future revision of that file. See also Publishing your formulas.
Next: The common.ulb file
See Also
Classes
Inheritance
Class parameters
341
The common.ulb file
Classes can be useful on their own, but they show their true power when you combine them with
each other. When used well, classes can eliminate duplicate code in everyone's formulas. However,
to realize this potential, there needs to be a common foundation so all classes can work with each
other easily.
The common.ulb file installed in the Public formula folder provides such a foundation. It contains an
extensive collection of base classes and utility classes. Here is a quick overview of the most
important classes:
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The Array classes provide a way to pass arrays to functions, since Ultra Fractal doesn't allow
this directly. See also Function arguments.
The Generator and IntegerGenerator classes are base classes for objects that generate a
sequence of values, such as random number generators.
The Transfer and IntegerTransfer classes are base classes for objects that take a value and
transform it.
The Formula class and descendants such ConvergentFormula, DivergentFormula and
ConvergentDivergentFormula wrap a complex fractal formula as an object. See Example 1 Formula classes for an example of how this works in practice.
The Coloring, GradientColoring and DirectColoring classes wrap coloring algorithms as an
object.
The Transform, UserTransform and ClipShape classes wrap transformations as an object.
The TrapShape, TrapMode, TrapColoring, TrapPosition, TrapTransfer and ColorTrap classes
provide a framework to implement orbit trap coloring algorithms where every aspect of the
algorithm is extensible. See Example 2 - Orbit trap classes.
The goal is to provide flexible base classes that help formula authors to write classes and formulas
that work with all other classes. It is highly recommended to read through the common.ulb file
thoroughly before you start writing your own classes. Also have a look at how the standard classes in
Standard.ulb are implemented.
The common.ulb file will be continually updated via the online formula database. The UFprogrammers mailing list is the best place to discuss the library of classes and to suggest
modifications.
Documentation for the common.ulb file and any other classes in the online formula database is
accessible via formulas.ultrafractal.com/reference.
Next: Memory management
See Also
Classes
Importing classes
342
Memory management
Ultra Fractal manages the memory for all objects that are created automatically, and normally you
do not have to worry about this. However, if you create a large number of objects, or if your objects
are large because they use large arrays, you might want to know how you can influence memory
usage during a calculation.
The lifetime of an object is managed with reference counting. As long as there is a reference to an
object, it will not be freed. If the last reference to an object goes out of scope, if another object is
stored to the reference, or if it is set to 0, the object is freed immediately.
For debugging purposes, you can print the name and reference count of an object. This example
uses the Point example class:
Point p = new Point(0, 0)
print(p)
; Prints Point (1)
Point pt2 = p ; Create a second reference
print(p)
; Prints Point (2)
p = 0
; Clears the first reference
print(pt2)
; Prints Point (1)
pt2 = 0
; Frees the Point object
print(pt2)
; Prints 0
As you can see, you can free an object by setting all reference that point to it to 0, the null
reference. You can use this to reclaim memory during a calculation.
When using recursive data structures, you can easily get the situation where two objects contain
references to each other. In this case, the reference count of both objects will never reach zero. To
solve this, Ultra Fractal keeps a running list of all live objects and will free them once the entire
calculation is finished. If you need to reclaim memory earlier, you need to explicitly set the
references to 0 so the objects can be freed. You could say that Ultra Fractal uses deterministic
garbage collection, in contrast to environments like Java or .NET which use nondeterministic garbage
collection.
Again, normally you do not have to worry about this because the amount of memory consumed by
objects is usually very modest. But in case memory usage becomes a problem, you can use this
information to track down the reference counts of objects and make sure they are freed when
necessary.
Next: Writing transformations
See Also
Classes
Objects
343
Writing transformations
Transformations are put in transformation files with the .uxf extension. They can have the following
sections, in this order:
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●
global
transform
default
If a transformation does not start with a label, it is assumed to start with the transform section. The
optional setting within parentheses after the entry identifier is ignored.
The global section is executed only once per image and can be used to fill look-up tables and
initialize read-only variables. See Global sections.
The transform section contains one or more statements. The purpose of these statements is to take
the predefined symbol #pixel, which contains the coordinates of the pixel currently being calculated,
transform it and put the result back in #pixel. They can also set the predefined boolean symbol
#solid to true to give the pixel a solid color instead of calculating it. In this case, no further
calculations are done for the pixel. The solid color is adjustable on the Mapping tab of the Layer
Properties tool window.
The default section can contain the following settings:
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●
helpfile
helptopic
precision
rating
render
title
It can also contain one or more parameter blocks.
Next: Writing fractal formulas
See Also
Writing formulas
Transformations
344
Writing fractal formulas
Fractal formulas are put in fractal formula files with the .ufm extension. They can have the following
sections, in this order:
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●
global
builtin
init
loop
bailout
default
switch
If a fractal formula does not start with a label, it is assumed to start with the init section. If a fractal
formula contains an empty label (a single colon), it is assumed to start the loop section, and in this
case, the last statement in the loop section is assumed to be the boolean expression from the
bailout section (so the formula should not contain a separate bailout section). This set of rules
ensures compatibility with old Fractint formula. It is not recommended to use this when writing new
formulas, though.
The optional setting within parentheses after the entry identifier specifies the symmetry of the fractal
formula. See Symmetry.
The global section is executed only once per image and can be used to fill look-up tables and
initialize read-only variables. See Global sections.
The builtin section is used for accessing built-in fractal formulas. If this section is used, the global,
init, loop, and bailout sections are not allowed. The builtin section can contain the following
settings:
●
type
The init section is executed only once per pixel, and is useful for initializing variables.
The loop section is executed once per iteration. It should update the value of the predefined
complex variable z (you can also write to #z) using the old value of z.
The bailout section contains a single boolean expression. The loop section is repeated as long as
this expression evaluates to true (but it is always executed at least once).
The default section can contain the following settings:
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angle
center
helpfile
helptopic
magn
maxiter
method
periodicity
precision
rating
345
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render
skew
stretch
title
It can also contain one or more parameter blocks.
The switch section is used to implement switching from one formula type to another (for example
from Mandelbrot to Julia). See Switch feature.
Next: Writing coloring algorithms
See Also
Writing formulas
Fractal formulas
346
Writing coloring algorithms
Coloring algorithms are put in coloring algorithm files with the .ucl extension. They can have the
following sections, in this order:
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●
●
global
init
loop
final
default
If a coloring algorithm does not start with a label, it is assumed to start with the final section (in
that case, the init and loop sections are not allowed).
The optional setting within parentheses after the entry identifier specifies whether the coloring
algorithm can be used for inside coloring, outside coloring, or both. The possible values are:
INSIDE
The coloring algorithm is only intended for coloring the inside of a fractal.
OUTSIDE
The coloring algorithm is only intended for coloring the outside of a fractal.
If the setting is omitted, or has another value, the coloring algorithm is supposed to be useful for
both inside and outside coloring. See also Inside and outside.
The global section is executed only once per image and can be used to fill look-up tables and
initialize read-only variables. See Global sections.
The init section is executed only once per pixel, and is useful for initializing variables.
The loop section is executed once per iteration, right after the loop section of the fractal formula
has been executed. It can read the current value of #z and perform some calculations on it.
The final section is executed afterwards to determine the actual index into the gradient (this index is
further transformed by the various settings on the Inside or Outside tabs). The index is a float value
and should be written to the predefined symbol #index. If the settings on the Inside or Outside tab
are set to their default values (Density = 1, Transfer = Normal and Offset = 0), the entire gradient
range corresponds to the range 0..1 of the index value.
To create a direct coloring algorithm, use the predefined symbol #color instead of #index.
It is also possible to set the predefined symbol #solid to true: this gives the pixel the solid color set
in the Inside or Outside tab of the Layer Properties tool window.
The default section can contain the following settings:
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helpfile
helptopic
precision
rating
render
title
347
It can also contain one or more parameter blocks.
Next: Writing direct coloring algorithms
See Also
Writing formulas
Coloring algorithms
348
Writing direct coloring algorithms
Direct coloring algorithms directly output a color instead of an index value. This is done by assigning
a value to the #color predefined symbol instead of to #index.
To compute this color, you can use color expressions, color variables, and color arithmetic. The
following arithmetic operations are available:
c1 + c2
Returns a color where each component is the sum of the respective components
from c1 and c2. So, red(c1 + c2) is equal to red(c1) + red(c2).
c1 - c2
Subtracts the color components in c2 from the respective color components in c1.
So, red(c1 - c2) is equal to red(c1) - red(c2).
c*f
Multiplies each component of c with a float value. So, red(c * f) is equal to red(c)
* f. Note: the float value must be at the righthand side of the * operator.
c/f
Divides each component of c by a float value. So, red(c / f) is equal to red(c) / f.
For example, to calculate the average of two colors, use (c1 + c2) / 2. Be aware of the fact that the
alpha value is treated just like the other components. So, c / 2 will not only darken a color, it will
also make it more transparent.
The following conversion functions are available:
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●
●
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●
●
●
rgb
rgba
hsl
hsla
red
green
blue
hue
sat
lum
alpha
There are some functions for blending and retrieving gradient colors:
●
●
●
gradient
blend
compose
There are also functions to reproduce all layer merge modes. They are called mergeX, where X
stands for the name of the merge mode. See Merging functions.
You can use color parameters to let user specify a color. You can also use special user functions that
allow a user to select a merge mode. See Parameter blocks.
Next: Global sections
See Also
Writing coloring algorithms
349
Direct coloring algorithms
350
Global sections
Sometimes, initializing variables of a formula can require a large number of calculations. Since you
would normally initialize variables in the init section of a fractal formula or a coloring algorithm (or
the transform section of a transformation), these calculations are performed again and again for
every pixel.
Often, they only depend on parameter settings, and therefore the results are the same for every
pixel. To avoid doing many repeated calculations, you can move them to the global section. This is a
special section at the start of a formula that is executed once per image.
Use the global section to perform per-image calculations and store the results in variables that can
be read in other sections. Variables declared here are treated as read-only in other sections, so you
cannot use this to share variables across pixels (that would not work reliably).
In the following example, the global section is used to pre-calculate an array of random values that
is the same for every pixel. These random values are subsequently used to disturb a standard
Mandelbrot set.
MandelbrotModified {
global:
float values[#maxiter]
int i = 0
int seed = 12345678
while i < 100
seed = random(seed)
values[i] = seed / #randomrange
i = i + 1
endwhile
init:
z = (0,0)
int iter = 0 ; "i" is already taken
loop:
z = sqr(z) + #pixel + values[iter]
iter = iter + 1
bailout:
|z| 4
}
Notes
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●
Global sections are often combined with arrays to compute look-up tables that can speed up
the formula tremendously.
You can even declare an array equal to the size of the image (with the #width and #height
predefined symbols) and calculate the entire fractal in the global section of a coloring
algorithm. The final section is then used only to return colors or index values from this
array. This enables you to implement fractal types like IFS and flame fractals that are not
natively supported by Ultra Fractal. This technique does have some limitations: it can require
a fair amount of memory and the progress of the calculation is not reported. It is very slow
351
and memory-intensive with rendering to disk, especially with anti-aliasing, and it does not
work well with network calculations either. See also the render setting.
Next: Image parameters
See Also
Arrays
Sections
352
Image parameters
Formulas in Ultra Fractal can import external images. This is typically used only in direct coloring
algorithms, which can subsequently use the information from the image to return colors for each
pixel that is calculated. The standard Image coloring algorithm is a good example.
To be able to import an image, the formula needs to declare an image parameter. This takes the
form of a regular class parameter with the built-in Image class as the class type:
default:
...
Image param imageParam
caption = "Image"
endparam
The parameter block can contain the following settings: caption, enabled, hint, and visible. You
cannot specify a default image. By default, the image is always empty.
In the list of parameters in the Layer Properties tool window, the image parameter shows up as an
image preview and an Open button to select an image file. See Using images for an example. The
user can select any image from the computer and it will be loaded in the preview window.
To access the data from the image, you need to create an Image object from the image parameter,
just like with class parameters:
Image img = new @imageParam
int numPixels = img.getWidth() * img.getHeight()
You can now access all pixels in the image using the methods of the built-in Image class. The Image
object created is associated to the specified image parameter, so you can easily have multiple image
parameters if necessary.
Note: You can also create a stand-alone Image object with new Image. For example, you could
make a copy of an imported image and modify it.
Next: Random values
See Also
Classes
Image class
353
Random values
Some formulas need to calculate random values. Ultra Fractal offers two ways of obtaining pseudorandom values.
The predefined symbol #random returns a new complex random number for every pixel. This exists
primarily for compatibility with old Fractint formulas.
The preferred way of obtaining a random value is the random function. This function accepts an
integer seed and returns a new random seed. To generate a series of random numbers, you should
call the function repeatedly, each time supplying the seed returned by the previous call. Example:
int seed = 123456789 ; initial value
seed = random(seed)
; seed is now the first random number
seed = random(seed)
; seed is now the second random number
To obtain a random floating-point number between 0 and 1, divide abs(seed) by the predefined
symbol #randomrange. To obtain a random integer between 0 and n - 1, use abs(seed) % n.
You can generate multiple independent, reproducible series of random numbers just by declaring and
using multiple seeds. The random function will always return the same result for the same seed
value.
Next: Symmetry
See Also
Global sections
354
Symmetry
Some fractal formulas always create images that are symmetric. Ultra Fractal can take advantage of
the symmetry to speed up the calculation. To enable this, you must specify the symmetry of the
formula as the optional setting between parentheses right after the entry identifier. Example:
Mandelbrot(XAXIS) {
...
}
This formula is symmetric around the horizontal x-axis, therefore it uses the XAXIS setting. This
table lists all possible values for the symmetry setting:
XAXIS
Forces symmetry around the horizontal x-axis, or the real axis.
YAXIS
Forces symmetry around the vertical y-axis, or the imaginary axis.
XYAXIS
Forces symmetry around both the horizontal and the vertical axes.
ORIGIN
Forces rotational symmetry around the origin. This is useful for Julia sets.
PI
Not implemented.
You can append _NOPARM to all values (thus obtaining XAXIS_NOPARM, etc) to make sure
symmetry is only applied when all complex parameters are set to (0, 0). The XAXIS setting also
allows the suffixes _NOREAL and _NOIMAG to disable symmetry for non-zero real and imaginary
parts of all complex parameters.
Notes
●
●
Symmetry is always disabled if the rotation angle set in the Location tab is not zero, or if a
coloring algorithm that reads the value of #z is selected.
It is not recommended and not reliable to use this to enforce symmetry that does not exist in
the formula itself. It is only intended as a speed-up for formulas that naturally exhibit
symmetry.
Next: Switch feature
See Also
Writing fractal formulas
Formula files and entries
355
Switch feature
The switch feature allows you to switch easily between related fractal types. One fractal type can be
used as a map for another. This is very useful, since Mandelbrot sets, for example, are in fact maps
of the corresponding Julia sets.
To use the switch feature with your own formulas, you must include the switch section as the last
section in your fractal formula. Here is an example of a typical Mandelbrot formula using the switch
section:
Mandelbrot {
init:
z = 0
loop:
z = sqr(z) + #pixel
bailout:
|z| < @bailout
switch:
type = "Julia"
seed = #pixel
bailout = bailout
}
The type setting specifies the identifier of the formula (in the same file) to switch to. The other
settings can copy parameters and the pixel value from the source formula to the destination formula
(the formula Ultra Fractal is switching to). The #pixel symbol returns the coordinates of the point in
the fractal window where the user clicked to initiate the switch.
When switching, Ultra Fractal now loads the Julia formula, and tries to find the parameters seed and
bailout in the Julia formula. If these parameters can be found, they are set to the pixel value and
the bailout of the Mandelbrot formula. Otherwise, the settings are ignored.
So, you need to take the following steps to use the switch feature:
1. Append the switch section to the end of your formula.
2. Insert the type setting and use the entry identifier of the formula you want to switch to as
the setting value, enclosed in double quotes (like all string values).
3. Insert the setting "destination-parameter = #pixel" to let the switch feature be dependent on
the point where the user clicked inside the fractal window. If you want, you can use this
setting more than once, or just leave it out. The parameter in the destination formula must
be complex, otherwise this setting is ignored.
4. Optionally, insert additional settings "destination-parameter = source-parameter" to copy
other parameters from the source formula to the destination formula. Be sure that the types
of the source and destination parameters are the same; otherwise, the setting is ignored.
Parameters not explicitly copied here are set to the default values.
Here is an example of a Julia formula that could be used with the Mandelbrot formula shown above.
Note that the Julia formula allows you to switch back to the Mandelbrot formula (of course without
using the pixel value).
356
Julia {
init:
z = #pixel
loop:
z = sqr(z) + @seed
bailout:
|z| < @bailout
switch:
type = "Mandelbrot"
bailout = bailout
}
Next: Providing help and hints
See Also
Writing fractal formulas
Switch mode
357
Providing help and hints
To make your formulas easier to use, you might want to add help. There are two ways to provide
help for formulas.
The easiest way to add help to your formula is to provide hints for all parameters. A hint is a small
explanatory message that is shown in the Fractal Mode tool window when the user hovers over the
paramter, or when the user clicks the ? button in the title bar of the Layer Properties tool window,
and then clicks the parameter.
●
To add a hint to a parameter, use the hint setting in the parameter block.
Although parameter hints are certainly helpful, they cannot provide an overview of the purpose and
intended use of the formula. To overcome this, you can create a separate help file and specify its
name and location in the formula file so Ultra Fractal can open it.
Ultra Fractal supports help in HTML files, in Windows Help files (*.hlp), in Windows HTML Help files
(*.chm), in Adobe Acrobat files (*.pdf), in Microsoft Word files (*.doc), and in plain text files (*.txt).
These help files are usually installed in the Help on Formulas folder. By default, its location is "My
Documents\Ultra Fractal 5\Help on Formulas", but you can change this in the Folders tab of the
Options dialog.
●
To link a formula to an external help file, use the helpfile and helptopic settings in the
default section.
Ultra Fractal launches the help file when the user clicks the Help button in the Layer Properties tool
window.
Next: Debugging
See Also
Publishing your formulas
Parameter blocks
358
Debugging
When you are writing complex formulas, it is likely that they will not immediately function as
intended. Although the compiler tries to catch most of the common mistakes and reports them as
errors or warnings, some mistakes will go unnoticed until you try the formula.
The process of trying a formula and correcting it until it works is called debugging, because you are
essentially removing bugs (programming mistakes). To debug a formula, you use run-time
messages.
Run-time messages can be generated by a formula while it is executed. They appear in the Compiler
Messages tool window, where you can examine them.
To enable run-time messages, define the DEBUG symbol. Run-time messages are caused by an
array index that is out of bounds, an assignment of incompatible arrays, or by the print function.
Here is an example:
int a[4]
int i = 5
a[i] = 4
print("Hello?")
$define DEBUG
a[i] = 3
print("Hello, world")
; out of bounds, no run-time message
; ignored
; out of bounds, causes run-time message
; causes run-time message
Use the print function to examine the values of variables while the formula is executed, so you can
understand why it is not working properly.
By not defining the DEBUG symbol, run-time messages are not generated. When you are publishing
a formula, you should make sure the DEBUG symbol is not defined, since the users of your formula
will probably not appreciate the run-time messages.
Next: Optimizations
See Also
print function
Compiler directives
Memory management
359
Optimizations
The compiler performs optimizations to make sure that all formulas run as fast as possible. It is
helpful to know something about these optimizations when writing formulas.
The optimizations can be divided into two categories:
●
●
Evaluation of constant expressions. Constant expressions are expressions whose value can
be evaluated by the compiler. Constant expressions can contain operators, built-in functions,
constants and parameters. This is possible because the formula is re-compiled each time a
parameter changes, so parameters can be treated as constants by the compiler.
Replacement of slow operations by faster ones, such as replacing 2*x by x+x (adding is
faster than multiplying).
When writing formulas, this has the following consequences:
●
●
●
●
Writing to parameters is not recommended. This can make the formula run slower, because
parameters cannot be treated as constants anymore.
You can write constant expressions wherever you want. You do not have to precalculate
them, because the compiler can do that for you. So, using 2 + 1/3 is just as fast as using
2.3333. Just use whatever you find most convenient.
If statements with constant expressions (like if 3 < 2) are completely eliminated by the
compiler. This is very helpful when you use lots of if statements depending on the values of
enumerated parameters. Therefore making your formula versatile by providing many options
does not cause it to run slower.
You can use descriptive operators like z^4 instead of z*z*z*z or sqr(sqr(z)), since Ultra
Fractal automatically chooses the most efficient operation independent of the operators or
functions used.
Next: Compatibility
See Also
Conditionals
360
Compatibility
Ultra Fractal 5 accepts almost all formulas written for earlier versions of Ultra Fractal. There are
many changes in the compiler since Ultra Fractal 4, but the language has been changed in such a
way that existing formulas will still compile. The new language features are accessed with semireserved keywords, meaning that you can still use them as variable names. This ensures that there
will not be a conflict with existing formulas.
There are some minor differences in the compiler since Ultra Fractal 2:
●
●
●
There are a three new keywords: color, heading, and endheading. Variables with these
names will have to be renamed. Parameters with these names should not be renamed to
avoid breaking backwards compatibility. Instead, add a @ character to the parameter name
in the parameter block that describes it, so the compiler will recognize it as a parameter, not
as a keyword. For example, "param color" should be changed to "param @color".
Some formulas might not run well with double precision (Ultra Fractal 2 always uses
extended precision). In this case, either correct the formula, or adjust the Additional
Precision value in the Formula tab of the Layer Properties tool window so extended
precision is used. You can verify this in the Statistics tool window. Also see Arbitrary
precision.
Built-in functions that can return complex values with float arguments are treated differently.
If the return value is assigned to a complex variable, the float argument is converted to
complex and the complex version of the function is called instead of the float version. This
fixes a number of bugs like:
complex c = sqrt(-1)
; should be (0, 1)
Unfortunately, sometimes it breaks backwards compatibility because Ultra Fractal 2 would
assign an invalid value to c in this case. To work around this, use:
float f = sqrt(-1)
complex c = f
The formula compiler is largely compatible with Fractint's parser and most Fractint formulas can be
used without modification. There are a few exceptions, however:
●
●
●
●
●
Writing to parameters is not recommended, since Ultra Fractal can perform special
optimizations when parameters are read-only. Formulas writing to parameters will be
accepted, though.
Writing to predefined symbols that are read-only, such as #pixel, is not allowed. Formulas
writing to these predefined symbols will not be accepted.
Formulas using the predefined symbol LastSqr will not be accepted. The usage of LastSqr
serves no purpose; it is intended as a speed-up but it only makes formulas run slower (even
in Fractint). Furthermore it makes formulas very hard to write and to understand.
Formulas using the function cosxx will not be accepted either. This function results from an
early version of Fractint which contained a bug in the cos function. The cosxx function allows
you to reproduce this bug in later versions of Fractint. If you still want to use the cosxx
function, you can write conj(cos(a)) instead of cosxx(a).
In Fractint, built-in functions with invalid arguments often return other values than in Ultra
Fractal. For example. log(0) returns 0 in Fractint, but it returns -infinity in Ultra Fractal. This
361
●
can cause problems. In general, if a Fractint formula gives a blank screen instead of a
fractal, you should check the formula for this kind of errors (log(0), division by zero,
recip(0), etc).
Fractint iterates fractal formulas not the number of times given by the maximum iterations
value, but one time less. Ultra Fractal does iterate fractal formulas the number of times
given by the maximum iterations value. The Fractint PAR import feature in Ultra Fractal
takes this into account and subtracts one from the maximum iterations value used by
Fractint.
Generally, formulas that depend on the forgiving behaviour of Fractint's parser will not be accepted.
Often Fractint accepts formulas that contain syntax errors and it will still produce a picture. Ultra
Fractal will refuse to load such formulas. This is useful, because it helps you to write clear and
understandable formulas, and it might point you in the direction of possible errors.
Next: Execution sequence
See Also
Invalid operations
362
Execution sequence
To help you understand the way Ultra Fractal executes the various sections in all formula types, here is an
overview of the execution sequence per pixel, written in pseudo-code similar to the formula language.
Before calculating the image, the global sections are executed:
for each transformation
execute global section of transformation
execute global section of fractal formula
execute global section of inside coloring algorithm
execute global section of outside coloring algorithm
Then, for each pixel, the following calculations are performed:
for each transformation
#solid = false
execute transform section of transformation
if #solid == true
stop and give pixel the solid mapping color
endfor
execute init section of fractal formula
execute init section of inside coloring algorithm (if it exists)
execute init section of outside coloring algorithm (if it exists)
int iter = 0
repeat
execute loop section of fractal formula
bool b = the expression in the bailout section of the fractal formula
if b == true
; not yet bailed out
execute loop section of inside coloring algorithm (if it exists)
execute loop section of outside coloring algorithm (if it exists)
endif
iter = iter + 1
until (b == false) || (iter == #maxiter)
#numiter = iter
if #numiter == #maxiter
; pixel is inside
execute final section of the inside coloring algorithm
else
; pixel is outside
execute final section of the outside coloring algorithm
endif
color the pixel
Next: Invalid operations
See Also
Writing transformations
363
Writing fractal formulas
Writing coloring algorithms
Global sections
364
Invalid operations
Formulas can easily perform invalid operations, such as dividing by zero. Rather than showing an
error message when an invalid operation occurs, Ultra Fractal just ignores the error and calculates
further. This means that the resulting image can be unpredictable if you do not pay proper attention
to these special cases. See also the isInf and isNaN functions, and Compatibility.
Invalid operations include dividing by zero (also with the % operator), and using some built-in
functions with invalid arguments. The range of valid arguments for a function is always discussed (if
there are invalid values) in the description of the function. It does not hurt to use arguments outside
the valid range, as long as you remember that the results may be unpredictable.
If you are using loops, you should avoid writing infinite loops at all times. An infinite loop is a loop
which repeats forever, without stopping. Here is are two examples:
while true
...
endwhile
repeat
...
until false
You must make sure that the loop is exited at some time. This means that the condition in a while
loop should eventually become false, and that the condition in a repeat loop should eventually
become true.
If, for some reason, the formula still enters an infinite loop, the fractal window will remain black and
no pixels will be calculated at all because the formula is still busy to calculate the first pixel, which
will never be finished. Ultra Fractal is still able to terminate an infinite loop. Just close the fractal
window, or select another formula.
Next: Publishing your formulas
See Also
Debugging
365
Publishing your formulas
When you have written a new formula, you might want to publish it, so other people can use it as
well. You can publish it using the online formula database at formulas.ultrafractal.com. When you
register with the formula database, you reserve a two- or three-letter abbreviation that you can use
to name your formula files.
Before publishing your formula, take a step back and ask yourself the following questions:
●
●
●
Does your new formula add something that is not already available in the formula database?
In other words, is it worth trying for other people?
Have you carefully considered all parameters and the effect that they have? Usually,
formulas with fewer parameters are more effective and easier to use. Don't add extra
parameters just because they look interesting.
Have you added help and hints to make your formula easier to use?
In general, you should take responsibility for the formulas that you publish. For complex formulas,
you might want to have them beta-tested by a small group of people first. Consider that it might not
be possible to fix problems later without breaking compatibility with parameter sets produced by
earlier versions.
When you are revising and improving your formula files, make sure that you do not break backwards
compatibility either. Here are some guidelines to help you:
●
●
●
●
Do not give the formula a different entry identifier, unless you know what you are doing.
Parameter files reference the formula by its identifier, so they cannot be restored anymore if
the identifier has been changed. You can always change the title of the formula, of course.
Do not change the identifiers of existing parameters in your formula, since parameter sets
reference parameters in a formula by their identifiers. Instead, change their captions.
When using enumerated parameters, do not change the names of the existing items. It is
possible though to change their order and add new items without breaking existing
parameter sets.
When using classes and class parameters, see also Parameter forwards and Importing
classes.
See Also
Public formulas
Compatibility
366
General keyboard shortcuts
The following general keyboard shortcuts apply to any document window in Ultra Fractal, and some
can also be used when no document window is open at all.
Shortcut
Menu command
Description
Ctrl+N
File|New|Fractal
Creates a new fractal window.
Ctrl+O
File|Open
Opens an existing document file.
Ctrl+B
File|Browse
Opens a new browser window to open and
organize your documents.
Ctrl+D
File|Duplicate
Duplicates the active document window.
Ctrl+S
File|Save
Saves the active document.
F11
-
Toggles keyboard focus between the active
document window and the tool windows.
Ctrl+F11
Shift+Ctrl+F11
-
Moves keyboard focus between the tool
windows.
Shift+F2..F10
Window|Tool Windows
Shows and hides a tool window.
F12
Options|Tool Windows
Shows and hides all tool windows.
F1
Help|Help
Shows context-sensitive help.
Shift+F1
Help|Contents
Shows the help table of contents.
Ctrl+F1
Help|Index
Shows the help index.
You can use several keyboard shortcuts with most input boxes for layer parameters. These are
shortcuts for the commands found in the right-click popup menu for the input box.
Shortcut
Popup menu
Description
Shift+Ctrl+K
Insert/Delete Key
Inserts a key for this parameter at the current
frame, or deletes the existing key. See Editing
animations.
Shift+Ctrl+X
Explore
Starts the Explore feature for this parameter.
Shift+Ctrl+E
Eyedropper
Starts the Eyedropper feature for this
parameter.
Shift+Ctrl+C
Copy Complex Value
For complex parameters, copies both the real
and imaginary value to the Clipboard so you
can transfer it to another complex parameter.
Shift+Ctrl+V
Paste Complex Value
Copies the complex value on the Clipboard to
this parameter.
Next: Keyboard shortcuts for fractal windows
See Also
Workspace
367
Keyboard shortcuts for fractal windows
The following keyboard shortcuts apply to fractal windows:
Shortcut
Menu command
Description
Ctrl+A
File|Save Parameters
Saves a parameter set describing the fractal.
See Parameter files.
Ctrl+E
File|Export Image
Exports the fractal as an image. See Exporting
and rendering.
Ctrl+Z
Edit|Undo
Undoes the last action. See Fractal history.
Ctrl+Y
Edit|Redo
Cancels the last Undo command.
Ctrl+C
Edit|Copy
Copies the parameter text of the fractal to the
Clipboard. See Copying and pasting.
Ctrl+I
Edit|Copy Image
Copies the image of the fractal to the
Clipboard.
Ctrl+V
Edit|Paste
Pastes the contents of the Clipboard into the
fractal.
F4
Fractal|Gradient
Shows the gradient editor to edit the colors of
the fractal.
F9
Fractal|Zoom In
Zooms in to the center.
F10
Fractal|Zoom Out
Zooms out of the center.
Ctrl+F
Fractal|Full Screen
Shows the fractal in full-screen mode.
F5
Fractal|Normal Mode
Selects Normal mode for zooming, panning,
and rotating by dragging the mouse.
F6
Fractal|Select Mode
Selects Select mode for zooming using a zoom
box.
F7
Fractal|Switch Mode
Selects Switch mode for switching to a related
fractal type.
Ctrl+R
Fractal|Render to Disk
Adds the fractal to the queue of render jobs.
See Rendering images.
Ctrl+1..4
Right-click,
Gradient|Randomize
Randomizes the gradient of the active layer.
Ctrl+J
Right-click, Gradient|Adjust
Colors
Adjusts the colors of the active layer.
Ctrl+]
Ctrl+[
Right-click, Gradient|Cycle
Colors
Cycles the colors in the active layer.
Ctrl+arrow keys
-
Pans the fractal in steps of one pixel.
Shift+Ctrl+arrow
keys
-
Pans the fractal in steps of ten pixels.
Next: Keyboard shortcuts in Select mode
See Also
General keyboard shortcuts
Fractal windows
368
Keyboard shortcuts in Select mode
The following keyboard shortcuts can be used in a fractal window when Select mode is active:
Shortcut
Description
Cursor left/right/up/down
Moves the selection box.
Shift+cursor up/down
Delete/Insert
Stretches the selection box.
Page Up
Shrinks the selection box.
Page Down
Enlarges the selection box.
Numeric keypad -/+
Rotates the selection box.
Home/End
Skews the selection box.
Enter
Zooms in.
Ctrl+Enter
Zooms out.
Esc
Cancels Select mode.
Hold down the Ctrl key for fine adjustments.
Next: Keyboard shortcuts for animations
See Also
Keyboard shortcuts for fractal windows
Fractal windows
369
Keyboard shortcuts for animations
Note: You need Ultra Fractal Animation Edition to work with animations.
The following keyboard shortcuts are used in fractal windows to create and edit animations:
Shortcut
Menu command
Description
F3
Animation|Animate
Enables or disables Animate mode.
Ctrl+Space
Animation|Play
Starts or stops animation playback.
Shift+Ctrl+<
Animation|Previous Key
Jumps to the first key to the left of the current
frame.
Shift+Ctrl+>
Animation|Next Key
Jumps to the first key to the right of the
current frame.
Ctrl+<
Animation|Previous Frame
Moves to the previous frame.
Ctrl+>
Animation|Next Frame
Moves to the next frame.
Ctrl+T
Animation|Timeline
Opens the Timeline tool window. This shortcut
also works in gradient editors.
The following keyboard shortcuts work in the Timeline tool window:
Shortcut
Description
Cursor up/down
Selects the first animated range above or below the current selection.
Cursor left/right
Selects the first animation key to the left or to the right of the current
selection.
Ctrl+Cursor
left/right
Moves the current selection to the left or right.
Ins
Toggles Insert mode. In Insert mode, click inside the timeline view to insert a
new animation key.
Del
Deletes the current selection.
Ctrl+T
Closes the Timeline tool window. This shortcut works as a toggle.
Next: Keyboard shortcuts for gradient editors
See Also
Keyboard shortcuts for fractal windows
Animation
Fractal windows
370
Keyboard shortcuts for gradient editors
The following keyboard shortcuts apply to gradient editors:
Shortcut
Menu command
Description
Ctrl+R
File|Replace
Opens an existing gradient, replacing the
current gradient.
Ctrl+Z
Edit|Undo
Undoes the last action.
Ctrl+Y
Edit|Redo
Cancels the last Undo command.
Ctrl+C
Edit|Copy
Copies the gradient to the Clipboard.
Ctrl+V
Edit|Paste
Pastes the contents of the Clipboard into the
gradient.
Ins
Edit|Insert
Inserts a new control point.
Ctrl+Del
Edit|Delete
Deletes the selected control points.
Ctrl+A
Edit|Select All
Selects all control points.
F4
Gradient|Fractal
Shows the fractal window that owns the
gradient editor. This shortcut works as a
toggle.
Ctrl+F2
Gradient|Color
Activates the color bars.
Ctrl+F3
Gradient|Opacity
Activates the opacity bar.
Ctrl+L
Gradient|Link Color and
Opacity
Links or unlinks the color and opacity bars. See
Transparent gradients.
F5..F8
Gradient|Randomize
Randomizes the gradient.
Ctrl+J
Gradient|Adjust Colors
Adjusts the color balance and brightness of the
gradient. See Adjusting gradients.
Ctrl+Enter
Right-click, Select Color
Selects the color of the selected control points.
Ctrl+Left
-
Selects the previous control point.
Ctrl+Right
-
Selects the next control point.
Hold down Ctrl while clicking in the gradient editor to add a new control point or to delete the
selected control point. When dragging control points, hold down Shift to constrain the movement to
horizontal or vertical only.
Next: Keyboard shortcuts for the Layer Properties tool window
See Also
General keyboard shortcuts
Gradients
371
Keyboard shortcuts for the Layer Properties tool window
The following keyboard shortcuts apply to the Layer Properties tool window. Most shortcuts work on
the active tab. Use Ctrl+Tab and Ctrl+Shift+Tab to activate other tabs.
Shortcut
Description
Ctrl+Alt+Enter
Opens the browser to select another fractal formula or coloring
algorithm.
Ctrl+Alt+R
Reloads the fractal formula, coloring algorithm, or selected
transformation.
Ctrl+Alt+E
Edits the fractal formula, coloring algorithm, or selected
transformation.
Ctrl+Alt+C
Copies the fractal formula, coloring algorithm, or selected
transformation (including parameter settings) to the Clipboard. If
the Location tab is active, the location is copied.
Ctrl+Alt+V
Pastes the contents of the Clipboard into the active tab.
Ctrl+Alt+Z
Resets the parameters of the fractal formula, coloring algorithm,
or selected transformation. If the Location tab is active, the
location of the active layer is reset.
Ctrl+Alt+F1
Shows help (if available) on the fractal formula, coloring
algorithm, or selected transformation.
Ctrl+Alt+A
Adds a new transformation.
Ctrl+Alt+D
Deletes the selected transformation.
Ctrl+Alt+T
Enables or disables the selected transformation.
F2
Renames the selected transformation.
Next: Keyboard shortcuts for the Fractal Properties tool window
See Also
General keyboard shortcuts
Formulas
Coloring algorithms
Transformations
372
Keyboard shortcuts for the Fractal Properties tool window
The following keyboard shortcuts apply to the Fractal Properties tool window:
Shortcut
Description
Shift+Alt+A
Duplicates the active layer or group and inserts the new copy in
the layers list.
Shift+Alt+G
Creates a new layer group and inserts it in the layers list.
Shift+Alt+D
Deletes the active layer.
Alt+Up
Activates the next layer.
Alt+Down
Activates the previous layer.
Shift+Alt+K
Turns the active layer into a mask for the layer above it, or turns
it into a normal layer again. See Masks.
Shift+Alt+O
Shows the transparency of the mask in grayscale, making it
easier to edit.
Shift+Alt+M
Selects the merge mode of the active layer.
Shift+Alt+1..9, 0, Left,
Changes the opacity of the active layer.
Right
Shift+Alt+F
Shows or hides the active layer.
Shift+Alt+E
Makes the active layer editable or not editable.
Shift+Alt+T
Turns layer transparency on and off. See Transparent layers.
F2
Renames the active layer.
Shift+Alt+Up
Moves the active layer one place up.
Shift+Alt+Down
Moves the active layer one place down.
Shift+Alt+C
Copies the active layer to the clipboard.
Shift+Alt+V
Pastes the contents of the Clipboard into the layers list.
When clicking on the Visible, Editable, or Transparent icons, hold down Shift to toggle all other
layers on and off.
Next: Keyboard shortcuts for formula editors
See Also
General keyboard shortcuts
Layers
373
Keyboard shortcuts for formula editors
The following keyboard shortcuts apply to formula editors:
Shortcut
Menu command
Description
Ctrl+P
File|Print
Prints the active document.
Ctrl+Z
Edit|Undo
Undoes the last action.
Ctrl+Y
Edit|Redo
Cancels the last Undo command.
Ctrl+X
Edit|Cut
Moves the selected text to the Clipboard.
Ctrl+C
Edit|Copy
Copies the selected text to the Clipboard.
Ctrl+V
Edit|Paste
Pastes the contents of the Clipboard into the
editor.
Ctrl+A
Edit|Select All
Selects all text.
Ctrl+F
Edit|Find
Finds text in the active document. See Finding
text and formulas.
Ctrl+H
Edit|Replace
Finds and replaces text in the active document.
Ctrl+G
Edit|Go to Line
Jumps to the specified line number.
Ctrl+E
Edit|Find Formulas
Finds formulas in the active document.
Shift+Ctrl+Cursor
up/down
Edit|Previous Section
Edit|Next Section
Jumps to the previous or next section in the
formula, for quick navigation.
Ctrl+I
Edit|Indent Block
Moves the selected text to the right. See
Indenting and commenting.
Ctrl+U
Edit|Outdent Block
Moves the selected text to the left.
Ctrl+L
Edit|Comment Block
Turns the selected text into a comment.
Ctrl+K
Edit|Uncomment Block
Turns the selected comment into normal text.
Ctrl+M
Insert|New Formula
Inserts a new formula.
Ctrl+J
Insert|Complete Template
Replaces text just before the cursor with the
corresponding code template. See Templates.
Ctrl+Q
-
Quickly jumps to another formula.
Help|Help
Searches for help on the word at the cursor
position. This works for reserved words, built-in
functions, predefined symbols, settings,
compiler directives, and labels.
F1
Next: Keyboard shortcuts for browsers
See Also
General keyboard shortcuts
Formula editors
374
Keyboard shortcuts for browsers
The following keyboard shortcuts apply to modeless browsers. Most shortcuts also work in modal
browsers.
Shortcut
Menu command
Description
Ctrl+X
Edit|Cut
Removes the selected items and copies them
to the Clipboard. The items are not actually
removed until you use the Paste command.
See Organizing your work.
Ctrl+C
Edit|Copy
Copies the selected items to the Clipboard.
Ctrl+V
Edit|Paste
Inserts the items you have copied or cut into
the selected location.
Ctrl+Del
Edit|Delete
Deletes the selected items.
F2
Edit|Rename
Renames the selected item.
Ctrl+A
Edit|Select All
Selects all items in the window.
Ctrl+I
Edit|Invert Selection
Reverses which items are selected and which
are not.
Ctrl+F
Edit|Find Entries
Finds entries in files. See Finding files and
entries.
Ctrl+L
View|Library Only
Shows the library folders only, or shows all
folders. See Library mode.
F5
View|Refresh
Refreshes the contents of the browser.
Ctrl+R
Right-click, Render to Disk
Renders the selected fractal file, parameter
file, or parameter set to disk. See Exporting
and rendering.
See Also
General keyboard shortcuts
Browsers
375
Purchasing Ultra Fractal
If you want to continue to use Ultra Fractal after the 30-day trial period, you must purchase it. You
will then receive a personal license key that turns your evaluation copy into a full registered version.
The full version does not mark exported and rendered images, and it does not show any evaluation
reminder dialog boxes. In addition, you are entitled to free support via e-mail and upgrades for a
reduced price.
Ultra Fractal 5 comes in two editions: the Standard Edition and the Animation Edition. The
difference is that the Animation Edition supports animations and network calculations, and the
Standard Edition does not. To verify the edition that you are currently using, click About on the Help
menu. If you own the Standard Edition, you can purchase an additional upgrade to the Animation
Edition.
You can place your order online via a secure server. All major credit cards and PayPal are supported.
To order, go to the Ultra Fractal web site:
●
Purchase Ultra Fractal
When your order is complete, your personal license key will be sent to you by e-mail in a few
minutes. Please contact [email protected] if you have any questions!
Next: Entering your license key
See Also
License information
Support
376
Entering your license key
After you have purchased Ultra Fractal, your personal license key will be sent to you via email in a
few minutes. This license key turns your evaluation copy of Ultra Fractal into a full version.
1. Start Ultra Fractal, and click Enter License in the Evaluation Reminder dialog that appears.
(Alternatively, click Enter License on the Purchase menu if Ultra Fractal is already opened.)
2. Copy and paste your license key from the email that you have received in the Enter License
dialog. Click Next to proceed.
3. If you are upgrading from an earlier version of Ultra Fractal, or if you have purchased an
upgrade from the Standard Edition to the Animation Edition, you will be prompted to enter a
previous license key as well. Ultra Fractal will search for previous license keys and fill them in
if possible. (Contact [email protected] if you have lost your previous license key.)
4. Click Restart to complete the registration process.
Be sure to make a backup of your license key, so you can enter it again in case you have to reinstall
Ultra Fractal, for example on a new computer.
Please contact [email protected] if you have any questions. Thank you for purchasing Ultra
Fractal 5!
Next: License information
See Also
Purchasing Ultra Fractal
Support
377
License information
If you purchase Ultra Fractal 5, you will receive a personal license. This personal license entitles you
to install and use the full version of Ultra Fractal 5 on any computer, as long as you are the only
person using the installed copies.
The license key that you receive upon purchasing Ultra Fractal 5 is personal and confidential. You
may not publish it, give it away, or sell it in any way. If you would like to introduce Ultra Fractal to
someone else, please point him or her to the Ultra Fractal web site at www.ultrafractal.com so he or
she can download a fresh evaluation copy.
In case you would like to purchase multiple copies of Ultra Fractal, for example for classroom use,
you can purchase a site license for a reduced price. Contact [email protected] for details and
pricing.
See Also
Purchasing Ultra Fractal
Support
378
Support
If you need help using Ultra Fractal, refer to the other topics in this help file first. You will usually find
the information you need here. Try to do some of the included tutorials if you are new to Ultra
Fractal. The help file is also available as a printable PDF manual on www.ultrafractal.com.
In case the online help does not solve your problem, ask a question on the public Ultra Fractal
mailing list. This is also a great place for sharing tips and parameter sets. See Mailing list.
To find links to tips, articles, and more tutorials, visit the Resources section on the Ultra Fractal web
site at www.ultrafractal.com. Also take a look at the FAQ page for answers to frequently asked
questions.
For technical support, you can also contact the author of Ultra Fractal via email at
[email protected]
Next: Mailing list
See Also
Getting help
Purchasing Ultra Fractal
Tutorials
379
Mailing list
The Ultra Fractal mailing list is a great place to ask questions and to share tips or fractal images with
other Ultra Fractal users. See www.ultrafractal.com/mailinglist.html for more information and
instructions for signing up.
For programming-related questions and discussion, there is a separate UF Programmers mailing list,
also accessible via the page above.
Warning: the mailing list generates about 20 to 50 messages per day. To make it easier to handle
this amount of messages, you can set up your e-mail software to automatically place messages
from the Ultra Fractal mailing list in a separate folder.
In Outlook Express, you can do this with Tools|Message Rules|Mail. In Mozilla Thunderbird, use
Tools|Message Filters. Messages from the Ultra Fractal list always contain [ultrafractal] in the
subject line, so that is a good way to identify them.
Next: Acknowledgements
See Also
Copying and pasting fractals
Copyright and tweaking
Support
380
Acknowledgements
First of all, I would like to thank the members of the beta test team for spending so much of their
time testing and evaluating Ultra Fractal 5 (in no particular order): Toby Marshall, Ken Childress,
Janet Parke, Jim Blue, David Makin, Ron Barnett, Kerry Mitchell, Jos Leys, Mark Townsend, Damien
Jones, Paul DeCelle and Linda Allison.
Special thanks go to Damien Jones for writing most of the common.ulb file and for hosting the Ultra
Fractal web site, the formula database, and the mailing list, and to Janet Parke for writing almost all
tutorials included in this help file.
Finally, I would like to thank all Ultra Fractal users for their continued support that enables me to
keep improving Ultra Fractal. I want to thank the formula authors in particular for publishing such a
wealth of formulas to the online formula database, which has made Ultra Fractal much more valuable
for everyone.
Ultra Fractal 5 was developed with Borland Delphi 7. Ultra Fractal uses the following third-party
libraries:
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The zlib compression library, written by Jean-Ioup Gailly and Mark Adler
The JPEG library, written by Jacques Nomssi Nzali
Indy internet components
FastMM memory manager
SynEdit and VirtualTree components
See Also
Support
381
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