Fractal Sculpture 03	Fractal Sculpture 12	Fractal Sculpture 21

The Fractal Sculpture example displays an Orbit Trap in the context of a symmetry transformation.

Experiment 1

Use the Preview Julia command to explore the Julia fractals for this example.

Experiment 2

Try out different Orbit Traps. To do this, select the Orbit Trap Map properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map

Change the Type property to one of the following:

• Circle
• Cross
• Epicycloid
• Fractal Gasket
• Gear
• Hypocycloid
• Isogonal Polygon
• Koch Triangle
• L-System
• Oscillator
• Penrose Kite
• Polygon
• Rectangle
• Rose
• Shape
• Sierpinski Triangle
• Spirolateral
• Star Polygon
• Triangle

Each of these orbit traps have properties (on the page found under the Orbit Trap Map page) to manipulate the trap and thereby change the resulting fractal.

You can also set the Type property to Instructions to access the set of built-in Orbit Traps.

To do this, set the Type property to Instructions and select the Instructions: Circle properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Circle

Change the Based On property to any of the built-in Orbit Traps.

Each of these programs have properties (on the Properties page found under the orbit trap) to manipulate the trap and thereby change the resulting fractal.

For this example, for the best results you will probably need to increase the Line Width property (if given) on the trap's properties page. Try a value 2 or 3 times larger than the default value. The rule of thumb is: if the resulting image is composed of lots of thin lines but no solid shapes, increase Line Width to create more interesting shapes, but if the resulting image is composed of a single large filled shape with few or no holes, decrease Line Width to see more detail.

Experiment 3

Try out different orbit trap blending algorithms. To do this, select the Orbit Trap Map properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map

Change the Blend property in the Orbit Trap Blend section to one of the other blends.

Experiment 4

Change the transformation applied to the orbit point prior to applying the symmetry transformation. To do this, 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.

Experiment 5

Change the transformation applied to the orbit point after to applying the symmetry transformation. To do this, 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.

Experiment 6

Change the transformation applied to the orbit point within the symmetry transformation. To do this, select the transformation's Properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Rotate
                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 7

Change the properties that control the symmetry transformation. To do this, select the transformation's Properties page:

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

Change any of these properties to define the symmetry transformation.

Experiment 8

Try a different symmetry transformation. To do this, select the Symmetry Transformation: Transformation Shift - Rotate page:

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

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.