Convergent Atan 2

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Convergent Atan 2 Examples

Fractal: Convergent Atan 2

Trifolium Stencil
Convergent Atan 2 01

Fractal: Convergent Atan 2

Rings of Convergence
Convergent Atan 2 02

Fractal: Convergent Atan 2

Medieval Necklace
Convergent Atan 2 03

The Convergent Atan 2 examples are Convergent Fractals that color the fractal using the angle associated with each sample point.

Note the following:

Example Fractal Type Fractal Equation
Convergent Atan 2 01 Julia Fractal Convergent Map 1
Convergent Atan 2 02 Julia Fractal Convergent Map 7
Convergent Atan 2 03 Julia Fractal Convergent Map 7

In the remaining sections, when I refer to the equation, I will use Convergent Map 1, 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 Generation section of the General page.

Play with the Fractal Equation's Properties

You can change the equation's properties for more variations.

Select the equation's properties page:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Convergent Map 1
            Properties

Play with the equation's properties.

Change the Julia Constant

You can generate other Julia Fractals based on the same equation.

Select the Fractal Equation:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Convergent Map 1

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: Convergent Map 4

Change the Based On property to one of the following Fractal Equations:

  • Convergent Map 1
  • Convergent Map 2
  • Convergent Map 3
  • Convergent Map 4
  • Convergent Map 5
  • Convergent Map 6
  • Convergent Map 7
  • Convergent Map 8
  • Convergent Map 9
  • Convergent Map 10
  • Convergent Map 11
  • Convergent Map 12
  • Convergent Map 13
  • Convergent Map 14

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 Working with Julia Fractals 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 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 apply a transformation to the fractal, select the Identity transformation:

General
    Mandelbrot / Julia / Newton
        Transformation
            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.

To add additional transformations, select Transformation:

General
    Mandelbrot / Julia / Newton
        Transformation

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
        Transformation
            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.

Play with Color

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

General
    Mandelbrot / Julia / Newton
        Classic
            Controllers
                Gradient Map - Atan 2
                    Properties

Play with the properties on this page to control the color mapping.

 

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