Orbit Trap

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Orbit Trap Examples

Depths of Color Orbit Trap 01	Ojo de Dios Orbit Trap 02	Chinese Dragon Orbit Trap 03
Who-ville Orbit Trap 06	Summer Solstice Orbit Trap 07	Winter Solstice Orbit Trap 08
Pewter Snowflake Orbit Trap 09	Seed of Life Orbit Trap 11	Spaceship Chaos Orbit Trap 12
Rites of Spring Orbit Trap 13	Aztec Throne Orbit Trap 14	Aztec Temple Orbit Trap 15
Extraterrestrial Condo Orbit Trap 16	Bronze Cross Orbit Trap 17	Multidimensional Gateway Orbit Trap 18
Solar Snowflake Orbit Trap 19	Spiral Mosaic Orbit Trap 21	Spiral Parade Orbit Trap 22
Tower of Babel Orbit Trap 23	Spiked Dragon Orbit Trap 24	Starburst Galaxy Coaster Orbit Trap 25
Spirolateralosaurus Orbit Trap 26	Winter Palace Orbit Trap 27

The Orbit Trap examples apply an Orbit Trap to a fractal based on various Fractal Equations.

Note the following:

In the remaining sections, when I refer to the equation, I will use Trig 13, but you should use the equation 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.

Remember that as you Zoom In, you may need to increase the Max Dwell property found in the Orbit Trap Orbit Generation section of the General page.

Explore the Julia Fractals

For the Mandelbrot Fractal examples, 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 the Julia Constant

For the Julia Fractal examples, you can generate other Julia Fractals based on the same equation.

Select the Fractal Equation:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Trig 13

Uncheck the Julia checkbox, 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.

Alternatively, you can change the Julia Constant property on the Fractal Equation page, and then click the Preview Fractal toolbar button on the Properties Window to generate a preview of your change in the Preview Window.

Change the Fractal Equation

You can change the Fractal Equation used to generate the fractal.

Select the Fractal Equation:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Trig 13

Change the Based On property to one of the other Fractal Equations.

Then 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 Preview Julia Support for details.

Remember to navigate to the properties page for the equation (found under the equation in the page hierarchy) and play with the different properties found there. Many of the equations support properties that can be used to generate lots of different variations.

Change the Orbit Trap

You can try out different Orbit Traps.

Select Orbit Trap Map:

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 try out the other built-in Orbit Trap programs.

Set Type to Instructions and then select Instructions: Circle:

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
• General Polygon
• Shape
• Sphere
• Patterned Sphere
• Solid Polygon
• Solid General Polygon
• Patterned Polygon
• Patterned General Polygon
• Epicycloid Polygon
• Hypocycloid Polygon
• Cross
• Crossed Lines
• Image
• Cassinian Curve
• Limacon
• Lemniscate
• Folium
• Cycloid of Ceva
• Circular Vine
• Celtic Knot
• Borromean Rings
• Tangent Circles
• Steiner Chain
• Rep-4 Tile
• Rep-4 Tile Patterned Polygon
• Rep-4 Tile Patterned General Polygon
• Rep-9 Tile
• Rep-9 Tile Patterned Polygon
• Rep-9 Tile Patterned General Polygon
• Polygon Motif
• Star of David
• String of Beads
• Wheel
• Ornament
• Sectors
• Triangles
• Star Polygon
• Faceted Polygon
• Composite Shape
• Spiral
• Daisy
• Swirl
• Flower
• Rose
• Super Ellipse
• 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 or are too complex to display in this context.

Change the Transformation

You can apply a transformation to the initial orbit point, or to each orbit point prior to passing it to the orbit trap.

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 initial orbit point, 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 change the transformation applied to each orbit point prior to passing it to the orbit trap, 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.

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