Steiner Chain Orbit Trap

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Steiner Chain Orbit Trap Examples

Fractal: Steiner Chain Orbit Trap

To infinity and beyond
Steiner Chain Orbit Trap 01

Fractal: Steiner Chain Orbit Trap

Interconnectivity
Steiner Chain Orbit Trap 02

Fractal: Steiner Chain Orbit Trap

Neural Net I
Steiner Chain Orbit Trap 03

Fractal: Steiner Chain Orbit Trap

Neural Net II
Steiner Chain Orbit Trap 04

Fractal: Steiner Chain Orbit Trap

Neural Net III
Steiner Chain Orbit Trap 05

Fractal: Steiner Chain Orbit Trap

Space Condo
Steiner Chain Orbit Trap 06

Fractal: Steiner Chain Orbit Trap

Megatropolis I
Steiner Chain Orbit Trap 07

Fractal: Steiner Chain Orbit Trap

Megatropolis II
Steiner Chain Orbit Trap 08

Fractal: Steiner Chain Orbit Trap

Crossroads
Steiner Chain Orbit Trap 09

Fractal: Steiner Chain Orbit Trap

Space Elevator
Steiner Chain Orbit Trap 10

Fractal: Steiner Chain Orbit Trap

Heavenly Sword
Steiner Chain Orbit Trap 11

Fractal: Steiner Chain Orbit Trap

Hourglass I
Steiner Chain Orbit Trap 12

Fractal: Steiner Chain Orbit Trap

Hourglass II
Steiner Chain Orbit Trap 13

Fractal: Steiner Chain Orbit Trap

Steiner's Dragon
Steiner Chain Orbit Trap 14

Fractal: Steiner Chain Orbit Trap

Red Dwarf
Steiner Chain Orbit Trap 15

Fractal: Steiner Chain Orbit Trap

Winter Star
Steiner Chain Orbit Trap 16

Fractal: Steiner Chain Orbit Trap

Steiner Scaffolding I
Steiner Chain Orbit Trap 17

Fractal: Steiner Chain Orbit Trap

Steiner Scaffolding II
Steiner Chain Orbit Trap 18

Fractal: Steiner Chain Orbit Trap

Steiner Scaffolding III
Steiner Chain Orbit Trap 19

Fractal: Steiner Chain Orbit Trap

North Star
Steiner Chain Orbit Trap 20

Fractal: Steiner Chain Orbit Trap

Bronze Lotus
Steiner Chain Orbit Trap 21

Fractal: Steiner Chain Orbit Trap

Meditation I
Steiner Chain Orbit Trap 22

Fractal: Steiner Chain Orbit Trap

Meditation II
Steiner Chain Orbit Trap 23

Fractal: Steiner Chain Orbit Trap

Meditation III
Steiner Chain Orbit Trap 24

Fractal: Steiner Chain Orbit Trap

Pipe Works I
Steiner Chain Orbit Trap 25

Fractal: Steiner Chain Orbit Trap

Pipe Works II
Steiner Chain Orbit Trap 26

Fractal: Steiner Chain Orbit Trap

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:

Example Fractal Type Fractal Equation
Steiner Chain Orbit Trap 01 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 02 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 03 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 04 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 05 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 06 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 07 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 08 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 09 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 10 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 11 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 12 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 13 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 14 Julia Fractal Exp 15
Steiner Chain Orbit Trap 15 Julia Fractal Trig 4
Steiner Chain Orbit Trap 16 Julia Fractal Trig 4
Steiner Chain Orbit Trap 17 Julia Fractal Exp 6
Steiner Chain Orbit Trap 18 Julia Fractal Exp 6
Steiner Chain Orbit Trap 19 Julia Fractal Exp 6
Steiner Chain Orbit Trap 20 Julia Fractal Trig 4
Steiner Chain Orbit Trap 21 Julia Fractal Trig 4
Steiner Chain Orbit Trap 22 Julia Fractal Trig 4
Steiner Chain Orbit Trap 23 Julia Fractal Trig 4
Steiner Chain Orbit Trap 24 Julia Fractal Trig 4
Steiner Chain Orbit Trap 25 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 26 Mandelbrot Fractal Mandelbrot
Steiner Chain Orbit Trap 27 Mandelbrot Fractal Mandelbrot

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:

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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