Apollonian Gasket Variations 01	Apollonian Gasket Variations 02

The Apollonian Gasket Variations example is an attractor based on a variation of the algorithm used to generate the Apollonian Gasket. Options are provided to select several different variants of the attractor.

Experiment 1

Select the properties to define the attractor. To do this, select the equation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Apollonian Gasket (Variations)
            Properties

Change the Variation property to 1 of the predefined variations or define your own by defining a Mobius transformation.

Change the Invert property to conjugate the results with the complex inversion transformation.

Experiment 2

Change the transformation applied to the base fractal. To do this, select the transformation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            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
    Orbital / IFS / Strange Attractor
        Transformation 1
            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.