Fractal Sculpture

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Fractal Sculpture Examples

Ceramic Lace
Fractal Sculpture 03

Apollonian Web
Fractal Sculpture 12

Butterfly Effect
Fractal Sculpture 21

The Fractal Sculpture examples display an Orbit Trap in the context of a symmetry transformation. The fractal is colored using a blend of Perlin Noise and a background pattern.

Note the following:

Example	Orbit Trap	Symmetry Transformation
Fractal Sculpture 03	Circle Inversion	Transformation Shift - Circular Path
Fractal Sculpture 12	Apollonian Gasket	Transformation Shift - Mobius Interpolation
Fractal Sculpture 21	Kleinian Group	Transformation Shift - Reflected Sectors

In the remaining sections, when I refer to the symmetry transformation, I will use Transformation Shift - Circular Path, but you should use the symmetry transformation for the example you are working with.

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.

Explore the Julia Fractals

Since these examples are Mandelbrot Fractals, you can use the Preview Julia command to explore the Mandelbrot's many different Julia Fractals. This is a common technique that can be used to generate lots of different Julia fractals from a single Mandelbrot image.

Execute the Home command on the View menu of the Fractal Window to reset the Mandelbrot fractal to the default position/magnification, and use the Preview Julia command to explore the Mandelbrot's many different Julia Fractals. See Working with Julia Fractals for details.

Change Transformation 1

You can change the transformation applied to the orbit point prior to applying the symmetry transformation.

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.

To change the transformation applied to the orbit point prior to applying the symmetry transformation, select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            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.

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.

Change Transformation 2

You can change the transformation applied to the orbit point after applying the symmetry transformation.

To change the transformation applied to the orbit point after applying the symmetry transformation, select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Transformation 2
                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.

Change the Transformation within the Symmetry Transformation

You can change the transformation applied to the orbit point within the symmetry transformation.

Select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Circular Path
                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.

Change the Properties for the Symmetry Transformation

You can change the properties that control the symmetry transformation.

Select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Circular Path
                Properties

Change any of these properties to define the symmetry transformation.

Change the Symmetry Transformation

You can try a different symmetry transformation.

Select the symmetry transformation:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Circular Path

Change the Based On property to one of the following symmetry transformations:

Transformation Shift - Rotate
Transformation Shift - Linear Path
Transformation Shift - Circular Path
Transformation Shift - Reflected Sectors
Transformation Shift - Mobius Interpolation

After selecting one of the symmetry transformations, select the transformation's properties page and change the properties found there.