Orbit Trap 01	Orbit Trap 02

The Orbit Trap example displays a circle Orbit Trap.

Experiment 1

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

Experiment 2

Try out different Fractal Equations. To do this, select the Fractal Equation: Mandelbrot properties page:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Mandelbrot

Change the Based On property to any of the different Fractal Equations. Note that a few of the equations do not lend themselves to an orbit trap representation (e.g., Barnsley, Julia Map). If the image does not look good, simply select another equation. Most equations look great when used with orbit traps.

For each equation you try, make sure to select the equation's Properties page (if found) and play with the different settings.

Experiment 3

Try out different Orbit Traps. To do this, select the Instructions: Circle properties page:

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

Change the Based On property to one of the following Orbit Traps:

• Circle
• Line
• Polygon
• Cross
• Crossed Lines
• Cassinian Curve
• Circular Vine
• Borromean Rings
• Tangent Circles
• Ornament
• Sectors
• Triangles
• Star Polygon
• Flower
• Rose
• Super Ellipse
• Sound Ornament
• Shapes
• Squares

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. There are several orbit traps not given in the above list since they are stand-alone fractals (e.g., Kleinian Group) or are too complex to display in this context (e.g., Complex Grid).

You can also try out the different optimized 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.

Experiment 4

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 5

Change the transformation applied to the orbit point prior to applying the trap. 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.