Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap Examples

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 01

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 02

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 03

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 04

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 05

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 06

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 07

Fractal: Epitrochoid Rose Orbit Trap

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Epitrochoid Rose Orbit Trap 08

 

The Epitrochoid Rose Orbit Trap examples are based on an Orbit Trap called the Epitrochoid Rose. The Epitrochoid Rose is a stand-alone curve. It is implemented as an Orbit Trap so it can take advantage of Orbit Trap related features in the Fractal Science Kit, but it does not need the normal orbit processing; i.e., I set the Max Dwell property found in the Orbit Trap Orbit Generation section on the Mandelbrot / Julia / Newton page, to 1, eliminating the normal orbit processing.

Change the Epitrochoid Rose Properties

Change the Epitrochoid Rose orbit trap properties.

Select the orbit trap's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Epitrochoid Rose
                    Properties

Play with the orbit trap's properties. The General Options are probably ok as they are. Try changing the Epitrochoid Options, the Rose Options, and the Combined Curve Options to affect the shape of the resulting curve.

Change the Orbit Trap

You can try out different Orbit Traps.

Select Instructions: Circle:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Epitrochoid Rose

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

  • Pythagorean Tree
  • Tiling
  • Limacon Net
  • Lemniscate Net
  • Nephroid Net
  • Epitrochoid Net
  • Hypotrochoid Net
  • Polygon Net
  • Polygon Whirl
  • Circle Web
  • String Art
  • Maurer Rose
  • Epitrochoid Rose
  • Farris Wheels Net
  • Harmonograph
  • Complex Grid
  • Circular Grid
  • Hexagon Grid
  • Shape Grid
  • Apollonius Grid
  • Parabolic Grid

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.

Change the Transformation

You can change the transformation applied to the orbit point prior to passing it to the orbit trap.

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
                Circle Inversion
                    Properties

Set the Center and Radius properties to define the circle of inversion.

You can also use a different transformation altogether. Select the Circle Inversion 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 add an additional transformation applied to each orbit point prior to passing it to the orbit trap, select Transformation 1:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Transformation 1

Click the New toolbar button to add a new Identity transformation to the bottom of the list, and then click the Move Up toolbar button to move the new transformation to the desired position in the list. Normally, I move the new transformation to the top of the list, but it can be placed anywhere. See Transformation Array for details.

Then select the Identity transformation:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Transformation 1
                Identity

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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