Steiner Chain Orbit Trap

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Steiner Chain Orbit Trap Examples

To infinity and beyond Steiner Chain Orbit Trap 01	Interconnectivity Steiner Chain Orbit Trap 02	Neural Net I Steiner Chain Orbit Trap 03
Neural Net II Steiner Chain Orbit Trap 04	Neural Net III Steiner Chain Orbit Trap 05	Space Condo Steiner Chain Orbit Trap 06
Megatropolis I Steiner Chain Orbit Trap 07	Megatropolis II Steiner Chain Orbit Trap 08	Crossroads Steiner Chain Orbit Trap 09
Space Elevator Steiner Chain Orbit Trap 10	Heavenly Sword Steiner Chain Orbit Trap 11	Hourglass I Steiner Chain Orbit Trap 12
Hourglass II Steiner Chain Orbit Trap 13	Steiner's Dragon Steiner Chain Orbit Trap 14	Red Dwarf Steiner Chain Orbit Trap 15
Winter Star Steiner Chain Orbit Trap 16	Steiner Scaffolding I Steiner Chain Orbit Trap 17	Steiner Scaffolding II Steiner Chain Orbit Trap 18
Steiner Scaffolding III Steiner Chain Orbit Trap 19	North Star Steiner Chain Orbit Trap 20	Bronze Lotus Steiner Chain Orbit Trap 21
Meditation I Steiner Chain Orbit Trap 22	Meditation II Steiner Chain Orbit Trap 23	Meditation III Steiner Chain Orbit Trap 24
Pipe Works I Steiner Chain Orbit Trap 25	Pipe Works II Steiner Chain Orbit Trap 26	Pipe Works III Steiner Chain Orbit Trap 27

The Steiner Chain Orbit Trap examples apply a Steiner Chain 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 4, 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 4

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 4

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 Steiner Chain Properties

Change the Steiner Chain orbit trap properties.

Select the orbit trap's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Steiner Chain
                    Properties

Change the Steiner Circle Options properties to change the orbit trap.

Change the Orbit Trap

You can try out different Orbit Traps.

Select Instructions: Steiner Chain:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Steiner Chain

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.

You can also try out the different optimized orbit traps. To do this, 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.

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.

Note that some of the examples are set to the Identity transformation rather than the Composite Function transformation:

General
    Mandelbrot / Julia / Newton
        Transformation
            Identity

For those examples, select the Identity 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.

Note that some of the examples are set to the Identity transformation rather than the Composite Function transformation:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Transformation 1
                Identity

For those examples, select the Identity 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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