Kleinian Group 02	Kleinian Group 11	Kleinian Group 13

The Kleinian Group example generates a Kleinian group Orbit Trap.

Experiment 1

Change the Kleinian group properties. To do this, select the Kleinian group's Properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Kleinian Group
                    Properties

Change the Example property to any of the different examples.

Some of the examples (e.g., Double Cusp examples) may require changes in several advanced properties (Depth, Radius Cutoff, Min Radius) to fill in the gaps between circles but many work well with the default settings.

Depth, Radius Cutoff, and Min Radius, control the number of circles that are generated to define the fractal. Depth is the depth of recursion used in the algorithm. Radius Cutoff is the minimum radius of circles placed on the processing stack and is used to terminate the recursion loop early on selected branches. Min Radius is the minimum radius required for a circle to be displayed.

You can increase Depth and/or decrease Radius Cutoff or Min Radius to fill in the gaps between circles but these changes can cause dramatic increases in processing time. If you make a change that seems to be taking forever, you should click the Cancel Display command on the Tools menu of the Fractal Window to terminate the processing. Then try adjusting these properties to reduce the processing (i.e., decrease Depth and/or increase Radius Cutoff or Min Radius).

Also, try changing the Recipe, Conjugate By, and/or UCG Transform properties. Using different combinations of these properties, you can generates many different designs.

Experiment 2

Change the textures mapped to the circles. To do this, select the Pattern Map - Texture properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Controllers
                Pattern Map - Texture

Use the Texture List Control to change the textures mapped to the circles. For this example, using 2 textures gives the best results. The Texture List Control allows you to add, remove, and reorder the textures in the list.