L-System Orbit Trap

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L-System Orbit Trap Examples

Fractal: L-System Orbit Trap

Hilbert's Gate
L-System Orbit Trap 01

Fractal: L-System Orbit Trap

Balance
L-System Orbit Trap 02

Fractal: L-System Orbit Trap

Compassion
L-System Orbit Trap 03

The L-System Orbit Trap examples are based on an L-System Orbit Trap. An L-System is defined using the L-System Language.

Change the L-System

You can change the L-System to one of the predefined L-System programs.

Select the L-System:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                L-System

You can set the Center, Radius, Angle, Order, and Line Width on this page. The Order controls the depth of recursion.

We are going to use one of the L-System fractals defined in the default L-System file Examples.l so we do not need to change the L-System File property. If you want to play with other L-System programs, you can find lots to choose from at the following pages:

Take some of these and either add them to the Examples.l file (found in the My Files folder) or place them in a separate file with the .l extension and then change the L-System File property to that file.

Note that L-System Orbit Trap 03 has 3 L-System entries and you can change any or all of them.

Next, select the L-System Instructions:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                L-System
                    L-System Instructions

Set the L-System property to one of the L-System programs.

Change the Transformation

You can apply a transformation to the fractal.

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 fractal, 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.

Change Transformation 1

Note: This section applies only to L-System Orbit Trap 02.

You can change the transformation applied to the orbit point prior to applying the symmetry transformation.

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.

Change Transformation 2

Note: This section applies only to L-System Orbit Trap 02.

You can change the transformation applied to the orbit point after applying the symmetry transformation.

Select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Transformation 2
                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.

Change the Transformation within the Symmetry Transformation

Note: This section applies only to L-System Orbit Trap 02.

You can change the transformation applied to the orbit point within the symmetry transformation.

Select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Linear Path
                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.

Change the Properties for the Symmetry Transformation

Note: This section applies only to L-System Orbit Trap 02.

You can change the properties that control the symmetry transformation.

Select the transformation's properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Linear Path
                Properties

Change any of these properties to define the symmetry transformation.

Change the Symmetry Transformation

Note: This section applies only to L-System Orbit Trap 02.

You can try a different symmetry transformation.

Select the symmetry transformation:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Symmetry Transformation: Transformation Shift - Linear Path

Change the Based On property to one of the following symmetry transformations:

  • Transformation Shift - Rotate
  • Transformation Shift - Linear Path
  • Transformation Shift - Circular Path
  • Transformation Shift - Reflected Sectors
  • Transformation Shift - Mobius Interpolation

After selecting one of the symmetry transformations, select the transformation's properties page and change the properties found there.

Play with Color

To play with color, select the color controller's properties page:

General
    Mandelbrot / Julia / Newton
        Classic
            Controllers
                Pattern Map - Perlin Noise
                    Properties

Change the Gradient Offset property to the 0-based index of the gradient you want to use. View the gradients on the Pattern Map - Perlin Noise page.

 

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