Schottky Group - Fractal Science Kit Example
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The Schottky Group example generates a Schottky group Orbit Trap.
Experiment 1
Change the Schottky group properties. To do this, select the Schottky group's Properties page:
General
Mandelbrot / Julia /
Newton
Orbit
Trap
Orbit Trap Map
Instructions: Schottky Group
Properties
Change the Type property to any of the different examples.
Also, try changing the Conjugate By and/or UCG Transform properties. Using different combinations of these properties, you can generates many different designs.
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.
Experiment 2
Change the transformation applied to the base fractal. To do this, select the transformation's Properties page:
General
Mandelbrot / Julia / Newton
Transformation
Composite
Function
Properties
Set the F(z) property to one of the complex functions in the list. You can change some of the other properties on this page for more variations.
Experiment 3
You can also try changing the transformation to one of the built-in Mobius transformations. Mobius transformations work especially well in this example because they preserve circles; circles are mapped to circles. Note that lines are considered circles with infinite radius.
To change the transformation to one of the built-in Mobius transformations, select the Composite Function page:
General
Mandelbrot / Julia / Newton
Transformation
Composite
Function
Set the Based On property to one of the following transformations:
- Mobius Transformation - Elliptic
- Mobius Transformation - Hyperbolic
- Mobius Transformation - Loxodromic
- Mobius Transformation - Parabolic
- Disc Automorphism - Elliptic
- Disc Automorphism - Hyperbolic
- Disc Automorphism - Parabolic
- Disc Automorphism - General
- Half-Plane to Disk
Note that the default for most of these transformations is the identity transformation so you will need to select the Properties page found under the transformation and change the properties in the section labeled Transformation Control.