Apollonian Gasket Orbit Trap

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Apollonian Gasket Orbit Trap Examples

Apollonian Necklace II Apollonian Gasket Orbit Trap 01	Apollonian Marble Screen I Apollonian Gasket Orbit Trap 02	Apollonian Marble Lattice Apollonian Gasket Orbit Trap 03
Apollonian Marble Mitosis Apollonian Gasket Orbit Trap 04	Apollonian Marble Screen II Apollonian Gasket Orbit Trap 05

The Apollonian Gasket Orbit Trap examples are based on an Orbit Trap called the Apollonian Gasket. The Apollonian Gasket is a stand-alone fractal. It is implemented as an Orbit Trap so it can take advantage of Orbit Trap related features in the Fractal Science Kit, but it does not need the normal orbit processing; i.e., I set the Max Dwell property found in the Orbit Trap Orbit Generation section on the Mandelbrot / Julia / Newton page, to 1, eliminating the normal orbit processing.

For these examples I modified the built-in Orbit Trap Apollonian Gasket to add the 2 silver border circles seen in the images.

The examples use complex Transformations to alter the fractal, and color the trap using a set of Perlin Noise based Orbit Trap Controllers to achieve the stone-like appearance. You can create lots of variations by changing the transformation applied to the fractal.

Zoom In/Out

Zoom In or Zoom Out to examine different parts of the fractal.

Execute the Home command on the View menu of the Fractal Window to reset the fractal to the default position/magnification, and then Zoom In to other areas.

Change the Transformation

You can apply a transformation to the fractal.

Execute the Home command on the View menu of the Fractal Window to reset the fractal to the default position/magnification before you adjust the transformation. Then change the transformation and Zoom In to interesting areas of the transformed image.

With the exception of Apollonian Gasket Orbit Trap 01, each of these examples applies a transformation to the fractal.

Apollonian Gasket Orbit Trap 02 applies the transformation Kaleidoscope - Triangles.
Apollonian Gasket Orbit Trap 03 applies the transformation Composite Function.
Apollonian Gasket Orbit Trap 04 applies the transformation Composite Function.
Apollonian Gasket Orbit Trap 05 applies 2 transformations: Kaleidoscope - Triangles and Composite Function.

In the following, when I refer to the transformation, I will use Composite Function, but you should use the transformation for the example you are working with.

To change the transformation applied to the fractal, 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.

You can also use a different transformation altogether. Select the Composite Function page, and change the Based On property to select a transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and play with the transformation's properties. See Transformation Support for details.

To add additional transformations, select Transformation:

General
Mandelbrot / Julia / Newton
Transformation

Click the New toolbar button to add a new Identity transformation to the bottom of the list. See Transformation Array for details.

Then select the Identity transformation:

General
    Mandelbrot / Julia / Newton
        Transformation
            Identity

Change the Based On property to select a transformation and then open the transformation's properties page (found under the transformation in the page hierarchy), and play with the transformation's properties. See Transformation Support for details.