Convergent Angle Relief	Convergent Atan 2 01	Convergent Atan 2 02
Convergent Orbit Trap 01	Convergent Orbit Trap 02

The Convergent fractal examples are:

• Convergent Angle Relief
• Convergent Atan 2
• Convergent Orbit Trap

These examples illustrate a few of the ways you can visualize Convergent fractals. Each example displays a Mandelbrot fractal based on a convergent fractal equation. Convergent Angle Relief adds a 3D relief based on the smoothed angle at each point. Convergent Atan 2 colors the fractal using the angle associated with each sample point. Convergent Orbit Trap displays the fractal using a circle Orbit Trap.

Experiment 1

Use the Preview Julia command to explore the Julia fractals for each example.

Experiment 2

Change the Fractal Equation to one of the other Convergent formulas. To do this, select the Fractal Equation: Convergent Map 1 properties page:

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

Note that Convergent Angle Relief example is based on Fractal Equation: Convergent Map 14.

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

These programs generate convergent fractals based on various equations. Each of these programs have properties (on the Properties page found under the equation) to manipulate the equation and thereby change the resulting fractal.

Experiment 3

For the Convergent Angle Relief example, you can change the coloring applied to the resulting image by setting the controller's properties. To do this, select the color controller's Properties page:

General
    Mandelbrot / Julia / Newton
        Classic
            Controllers
                Gradient Map - Angle Relief (Smooth Angle)
                    Properties

Change the Color Scheme to use a different gradient.

Change the Value property to Angle. This looks best if Factor is left at the default value of 1.

Change the Factor property to 2 or 3. This results in cycling through the color gradient 2 or 3 times, adding to the color complexity of the image. You can change the Power and/or Offset too for more variations.

These changes can be applied to the Mandelbrot or to any of the Julia fractals you create by clicking on the image in the Preview Window. A common approach is to execute the Preview Julia command and then click on the Mandelbrot until you get a Julia you like displayed in the preview window, then click on the Preview Window to open a full-sized version of the preview, open the Properties Window for the Julia, and then use the above techniques to adjust the Julia fractal's coloring.

Experiment 4

For the Convergent Atan 2 example, you can increase the complexity of the resulting image by setting the Repetitions property. To do this, select the color controller's Properties page:

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

Change the Repetitions property to 2.

Experiment with the other properties on this page too.

These changes can be applied to the Mandelbrot or to any of the Julia fractals you create by clicking on the image in the Preview Window. A common approach is to execute the Preview Julia command and then click on the Mandelbrot until you get a Julia you like displayed in the preview window, then click on the Preview Window to open a full-sized version of the preview, open the Properties Window for the Julia, and then use the above techniques to adjust the Julia fractal's coloring.

Experiment 5

For the Convergent Orbit Trap example, you can change the secondary coloring applied to the resulting image by setting the Triangle Metric property. To do this, select the Triangle Metric page:

General
    Triangle Metric

Change the Triangle Metric property in the p1 section. The other properties on this page also affect the resulting triangle metric point. When you have time, read the Triangle Metric page documentation for details. For now, ignore these other properties.

A second way to affect the secondary coloring applied to the resulting image is by setting the Factor property. To do this, select the color controller's Properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Controllers
                Gradient Map - Value Sum
                    Properties

Change the Factor property in the Value 2 section.

Either of these methods can be applied to the Mandelbrot or to any of the Julia fractals you create by clicking on the image in the Preview Window. A common approach is to execute the Preview Julia command and then click on the Mandelbrot until you get a Julia you like displayed in the preview window, then click on the Preview Window to open a full-sized version of the preview, open the Properties Window for the Julia, and then use the above techniques to adjust the Julia fractal's coloring.

Experiment 6

Change the transformation applied to the base fractal. To do this, 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.

Experiment 7

For the Convergent Orbit Trap example, you can change the transformation applied to the orbit point prior to applying the trap. To do this, 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.