Angle Relief x2	Angle Relief y2	Apollonian Gasket Variations 01
Apollonian Gasket Variations 02	Circle Orbit Trap 05	Circle Orbit Trap 06
Circle Orbit Trap 10	Complex Analysis	Convergent Angle Relief
Convergent Atan 2 01	Convergent Atan 2 02	Convergent Orbit Trap 01
Convergent Orbit Trap 02	Direct Color 01	Direct Color 02
Fractal Sculpture 03	Fractal Sculpture 12	Fractal Sculpture 21
Isogonal Polygon Orbit Trap 01	Isogonal Polygon Orbit Trap 02	Isogonal Polygon Orbit Trap 03
Julia Map 01	Julia Map 02	Julia Map 03
Kaleidoscope 02	Kaleidoscope 07	Kaleidoscope 09
Kleinian Group 02	Kleinian Group 11	Kleinian Group 13
Kleinian Group Attractor	L-System Classic	L-System Orbit Trap
L-System Shift	Newton Angle Relief	Newton Classic
Newton Orbit Trap	Newton Shift	Newton Trap Relief
Orbit Trap 01	Orbit Trap 02	Ornament
Phoenix	Quadratic Attractor	Rep-9 Tile
Schottky Group 03	Schottky Group 04	Schottky Group 11
Sierpinski Cycloid	Sierpinski Variations	Symmetric Attractor 01
Symmetric Attractor 03	Symmetric Attractor 04	Symmetric Icon

Each image was created from the named example by performing 1 or more of the experiments given in the example's description, resizing the image to 800x600, and enabling high-quality image processing. I have included in the download both the properties files for the examples and the properties files used to generate the above images. The files used to produce the images are in a folder named Experiments under the folder containing the examples.

Additionally, I have included a folder named Gallery in the download, that contains the fractal properties files that I used to generate many of the images in my deviantART gallery and in my photo albums on Facebook, Flickr, and MySpace. You can use these files as a starting point for your own explorations. See the Gallery section below for recommendations for working with the Gallery files.

Fractal Science Kit Examples Overview

Fractal properties files are saved as XML files. In the following discussions, when referring to the example files, the .xml suffix is omitted for brevity.

Once the examples are in place, you can open them by executing the Open File command on the File menu of the Fractal Window.

When the Open XML File dialog is displayed, open the folder containing the example files, select one of the examples, and click Open to load the file. A message box is displayed to ask if you want to replace the properties in the existing window or open a new window. Click Yes to replace the properties in the existing window. Finally, click Display Fractal on the Tools menu to display the example.

The following pages describe the Fractal Science Kit examples:

• Angle Relief
• Apollonian Gasket Variations
• Circle Orbit Trap
• Complex Analysis
• Convergent
• Direct Color
• Fractal Sculpture
• Isogonal Polygon Orbit Trap
• Julia Map
• Kaleidoscope
• Kleinian Group
• Kleinian Group Attractor
• L-System
• Newton
• Orbit Trap
• Ornament
• Phoenix
• Quadratic Attractor
• Rep-9 Tile
• Schottky Group
• Sierpinski Cycloid
• Sierpinski Variations
• Symmetric Attractor
• Symmetric Icon

Each page contains a description of 1 or more examples and several experiments that you can use to generate numerous additional fractals based on the given example. The example descriptions and the associated experiments are not as detailed as those in the Tutorials and I recommend that you work through the Tutorials first so that you have a basic understanding of the application windows and the property page hierarchy. At a minimum, you should read the 1^st page of the Tutorials which contains a few concepts necessary to understand the example descriptions.

The following sections cover a few important topics related to all of the examples.

Properties Pages

Each of the experiments given in the example descriptions provide instructions for navigating to 1 or more Properties Pages and changing the example's properties to affect the fractal image in some way. The Properties Window is used to access the Properties Pages associated with a fractal. There is a separate Properties Window for each Fractal Window.

To view the Properties Pages for the fractal, open the Properties Window by executing the Properties Window command on the View menu.

After making changes to 1 or more Properties Pages, you can view the resulting fractal image by executing the Display Fractal command on the Tools menu.

Typically, you will open the Properties Window, make changes to 1 or more Properties Pages, and generate a new fractal image by executing the Display Fractal command on the Tools menu of the Fractal Window. Then you can make additional changes to the Properties Pages, generate a new fractal image, and so on. If you see something interesting along the way, you can Zoom In to see more detail, or enable high-quality image processing to generate an image to save.

Note that you can save some time by executing the Preview Fractal command on the Tools menu of the Fractal Window (or by clicking the Preview Fractal button on the Properties Window toolbar) prior to executing the Display Fractal command. The Preview Fractal command generates a small preview of the fractal (in the Preview Window). If you like the preview, you can click on the image in the Preview Window and a new Fractal Window will open with a full-sized version of the preview. If you don't like the preview, you can move on to the next experiment without incurring the cost of displaying the full-sized image.

Preview Julia Support

Several of the descriptions for the Mandelbrot examples will instruct you to use the Preview Julia command to explore the Mandelbrot's associated Julia fractals. This is accomplished by selecting the Preview Julia item on the Tools menu of the Fractal Window.

When you select this item (or press the Preview Julia toolbar button), the Fractal Science Kit changes the cursor to a cross and places the Fractal Window into a state where clicking on the Mandelbrot fractal generates a Julia fractal preview in the Preview Window. The point on the Mandelbrot fractal where you click is used as the Julia Constant for the preview. There is a single Preview Window shared by all windows and each click on the Mandelbrot image generates a new Julia fractal preview, replacing any image currently in the Preview Window. If you wish to cancel the operation, simply select the menu item or toolbar button again. While you are in this state, the Preview Julia menu item has a check next to it and the Preview Julia toolbar button is depressed.

Try clicking at various points on the Mandelbrot fractal and view the resulting Julia fractals. The Julia fractal will be quite different depending on the characteristics of the point you click on. If you like the Julia preview, you can click on the image in the Preview Window and a new Fractal Window will open with a full-sized version of the preview.

Transformation Support

Several of the example descriptions include experiments to apply a transformation to the fractal. Most of these examples use the Composite Function transformation since it is flexible, efficient, and easy to use. This transformation allows you to define a composite function from 2 complex functions. When selecting a complex function on the program's Properties page, you should skip over the first several functions in the list and start experimenting with the Pow2 function and above. The earlier functions tend to be uninteresting. You can change some of the other properties on this page for more variations.

There are lots of other transformations available that you can use as well but for the sake of brevity I have not described them here but feel free to try them out. Be sure to open the program's Properties page and try changing the transformation's properties for different results.

Some of the transformations are specialized programs useful only in certain situations. This is discussed in the comment section in the program's instructions. You can read the program comments or simply try to use the transformation and if it doesn't produce good results, try another one!

Texture Support

Several of the examples use textures to enhance the quality of the resulting fractal image. The textures included in these examples were generated using Genetica Viewer by Spiral Graphics. Genetica Viewer is a free application for rendering seamless textures that were created in Genetica. I highly recommend that you download Genetica Viewer. The download includes hundreds of seamless textures plus editing functionality to generate countless different variations of each texture.

Genetica Viewer is not required to view/execute the examples since I include the small set of textures required by the example programs in the distribution. However, if you want to use additional textures in your explorations, you will need to get them from somewhere, and I feel that Genetica Viewer is one of the best sources for seamless textures available.

It is important that the textures included in the examples distribution be located in a folder named Examples under the My Files folder. The reason this is required is that several of the examples reference textures found in the folder Examples\Textures under the My Files folder and they will not display properly if the textures are not found in that location.

Generating High-Quality Images

The examples are configured for exploration rather than for generating high-quality images. High-quality images take longer to generate than do lower quality images, so it is best to wait until you find an image you wish to save and then change the properties that affect the quality just before generating your final image so that you only incur the additional cost when necessary.

The most important property with respect to quality is Anti-Aliasing. Anti-Aliasing is a method used to improve the quality of the fractal image by oversampling the fractal and then averaging the results. The Mandelbrot examples have Oversampling set to <None> and you should increase Oversampling to 2x2 Oversampling or 3x3 Oversampling when you produce the final image.

This improves the quality of the resulting image but dramatically increases the space required for sample data and the time required to compute it. Note that 3x3 Oversampling is over twice as costly as 2x2 Oversampling so plan accordingly.

The Orbital examples have Oversampling set to 2x2 Oversampling or 3x3 Oversampling since anti-aliasing does not result in as severe a time penalty as with Mandelbrot fractals so you will not normally need to change this property in these cases.

Another way to improve the quality of the fractal is to modify the properties that control the orbit generation. For Mandelbrot fractals, the Orbit Generation properties (and Orbit Trap Orbit Generation properties for orbit trap based fractals) control the orbit generation process. Normally, the property settings in the examples are fine unless you zoom way into the fractal. In that case, you may need to increase Max Dwell to improve the quality near the Mandelbrot set boundary.

For Orbital fractals, the Orbital / IFS / Strange Attractor properties control the orbit generation process. typically, you will need to increase Max Count to increase the density of the samples if the Orbital fractal image appears too sparse, too dark, or too grainy. It is best to explore with Max Count set to 1 or 2 and then increase Max Count to 20 or 30 or more for the final image.

Finally, when working with Orbital fractals, you can try activating Adaptive Smoothing. This can sometimes improve an image that appears grainy or speckled.

Gallery

I have included a folder named Gallery in the download, that contains the fractal properties files that I used to generate many of the images in my deviantART gallery and in my photo albums on Facebook, Flickr, and MySpace. You can use these files as a starting point for your own explorations. This section give a few recommendations for working with the Gallery files.

Step 1: Choose a file to work with.

The first thing you need to do, is to choose a file to work with. The file Readme.txt, located in the same folder as the properties files, provides a list of the files and the names of the corresponding images used in the deviantART gallery or in the photo albums on Facebook, Flickr, and MySpace. You can find an image you like in one of the galleries, and using the name of the image, you can search the Readme.txt file to get the name of the corresponding properties file.

Another strategy is to open each properties file, and then use the Preview Fractal command to get a quick look at the fractal image without incurring the full cost of generating a large image.

Step 2: Reduce the quality settings.

Each of the properties files is configured to produce a high-quality image and it may take several minutes to generate the fractal. I recommend that you reduce the quality settings to improve the speed of the fractal generation. How you do this depends in large part on the type of the fractal you are working with.

When the fractal is a Mandelbrot Fractal, you should turn off Anti-Aliasing; i.e. set the Oversampling to <None>. In most cases, this change alone will dramatically improve the fractal generation performance by a factor of 10 or more. In rare cases, you may need to reduce the Max Dwell property found in the Orbit Generation section (or the Orbit Trap Orbit Generation section if the fractal is based on an Orbit Trap).

When the fractal is an Orbital Fractal, Anti-Aliasing should NOT be turned off. Since Orbital fractals do not generate an orbit per sample as do Mandelbrot fractals, anti-aliasing does not result in as severe a time penalty as with Mandelbrot fractals, and it is recommended that you set Oversampling to one of the higher settings when exploring Orbital fractals since the increased quality outweighs the cost. You can reduce the Oversampling to 2x2 Oversampling if you like, but you should rarely set it to <None>. Changing the Oversampling from 3x3 Oversampling to 2x2 Oversampling, for example, would cut both the time and memory required to generate the fractal by over 50%.

The way to dramatically improve the fractal generation performance when working with Orbital Fractals is to reduce the reduce Max Count property found in the Orbital / IFS / Strange Attractor section. For example, changing the Max Count from 100 to 10 will reduce the time required to generate the fractal by a factor of 10. Of course, the resulting image will not be as well defined and some parts may be hard to see.

You can speed up the image processing of some Orbital Fractals by turning off Adaptive Smoothing. Some of the gallery images use Adaptive Smoothing to improve grainy or speckled images that can result when generating many Orbital Fractals. Adaptive Smoothing attempts to improve the results by blurring the image using a low-pass filter. This processing takes time and you should turn off Adaptive Smoothing until you are ready to generate your final image.

Note that the processing time and memory allocation associated with a fractal are proportional with the size of the fractal image so you can both increase the speed and decrease the required memory by resizing the image.

Step 3: Explore

This step can take several different forms:

• Zoom In or Zoom Out to examine different parts of the fractal. Click Home to reset the image to the default position/magnification and then Zoom In to other areas. Remember that as you Zoom In, you may need to increase the Max Dwell property (found in the Orbit Generation section or the Orbit Trap Orbit Generation section if the fractal is based on an Orbit Trap) when working with Mandelbrot Fractals, or the Max Count property (found in the Orbital / IFS / Strange Attractor section) when working with Orbital Fractals.

• If the fractal is a Julia fractal, you can open the Fractal Equation page, uncheck the Julia checkbox, and generate the associated Mandelbrot fractal. Then click Home to reset the Mandelbrot to the default position/magnification and use the Preview Julia command to explore the Mandelbrot's many different Julia fractals. See the section Preview Julia Support above for details.

• If the fractal has defined an Orbit Trap, you can change the size, position, and other properties found on the orbit trap's properties page. These changes can have a dramatic effect on the resulting image. In addition, you can use a different orbit trap altogether. If the resulting image is too dense, try reducing the trap's line width and/or size. If the image is too sparse, try increasing the trap's line width and/or size.

• Add a Transformation (or replace/modify the existing transformation, if present). This is a common way to generate countless different images from the same fractal equation. Try out any/all of the available transformations and don't forget that most transformations have several properties you can adjust to obtain different results. Click Home to reset the image to the default position/magnification before you adjust the transformation, and then Zoom In to interesting areas of the transformed image.

• Adjust the properties of the associated Fractal Equation or Orbital Equation. Navigate to the properties page for the associated equation and play with the different properties found there. Many of the equations (especially the orbital equations) have rich sets of properties that can be used to generate lots of different variations.

• Use a different Fractal Equation or Orbital Equation.

• If the fractal is an Orbital Fractal (or a Mandelbrot Fractal that has defined an Orbit Trap), you can try adding a Symmetry Transformation.

Step 4: Increase the quality settings.

Once you find an image you wish to save, you can change the fractal properties to generate a high-quality image. High-quality images take longer to generate than do lower quality images, so it is best to wait until you find an image you wish to save and then change the properties that affect the quality just before generating your final image so that you only incur the additional cost when necessary.

See Generating High-Quality Images for details.

Step 5: Play with coloring.

At this point, I like to play with the image coloring. The Fractal Science Kit only regenerates the fractal data if you change a property that affects the fractal data, and the properties on the Color Controllers do not. Consequently, you can make changes on the Color Controllers and you will only need to remap the data to the image which takes a reasonably short amount of time compared to the actual fractal data generation. So you can change any of the controller's properties and/or gradients, or use a different controller altogether and incur only the cost of remapping the data to color. Other properties the do not affect the fractal data generation include data normalization, background color settings, embossing, image smoothing/sharpening, border coloring, and Adaptive Smoothing.

Step 6: Save your fractal

When you find an image you really like, you can save the fractal properties file (see Save Fractal Properties) and/or the fractal image (see Save Fractal Image).

Final words

Here are a few additional things to remember as you explore:

• The Preview Fractal toolbar button on the Properties Window generates a preview (in the Preview Window) of the fractal that would result if you were to execute the Display Fractal command on the associated Fractal Window. This is useful when you have made 1 or more changes to the properties and want a quick look at the effects of those changes without incurring the cost of redisplaying the fractal in the full window. The Preview Fractal command is also available on the Tools menu of the associated Fractal Window. If you click on the image in the Preview Window, a new Fractal Window will open with a full-sized version of the preview. See Preview Fractal and Preview Window for details.

• When you are about to Zoom In or Zoom Out and you want to preserve the current fractal, you can set up the Zoom In/Zoom Out box and then execute the Display Fractal in New Window command on the Tools menu of the Fractal Window. This generates a new Fractal Window based on the current values of all the properties associated with the existing Fractal Window and the zoom is applied to the new Fractal Window.

• When you click on the fractal image in the Fractal Window, information with respect to the sample point on which you clicked is displayed in the Information Window.  Click on Information Window on the View menu on the Fractal Window to view this information. This information is very useful when you are setting up the Color Controllers for a fractal in that you can click on different parts of the fractal and examine the data associated with the different points to guide your decisions with respect to mapping the data to color. For example, an orbit trap may assign different index values to different parts of the trap and you can use this to map different colors to the different parts. By clicking on the trap you can examine which parts have which index values to assist in the index to color mapping.

• The Open Documentation toolbar button opens the documentation in your browser to the page that describes the window or the currently selected properties page on the Properties Window. The Open Documentation toolbar button is a small round blue button with a question mark in the center and is the right-most toolbar button on most windows. Those windows that do not have the Open Documentation toolbar button usually have a Help button for this purpose.