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 01	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.

I would recommend that you start with the examples for your exploration. The examples are configured for exploration rather than for generating high-quality images and are much faster to generate. Another approach would be to start with the file used to produce one of the above images and reduce the quality settings to allow efficient display. For Mandelbrot fractals that usually means turning off Anti-Aliasing, and for Orbital fractals you would reduce Max Count (on the Orbital / IFS / Strange Attractor page).

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.