Angle Relief x2	Angle Relief y2

The Angle Relief fractal examples are:

• Angle Relief x2
• Angle Relief y2

These examples color the fractal using a 3D relief based on the angle at each sample point. Each example sets the Magnitude property in the Orbit Generation section of the Mandelbrot / Julia / Newton page and uses a color controller appropriate for the property setting. Angle Relief x2 sets Magnitude to x^2 and Angle Relief y2 sets Magnitude to y^2.

Experiment 1

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

Experiment 2

For the Angle Relief x2 example, you can change the Fractal Equation to one of several different equations. To do this, select the Fractal Equation: Exp 5 properties page:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Exp 5

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

• NanoGeometry 1
• NanoGeometry 4
• NanoGeometry 5
• Trig 2
• Trig 11
• Trig 17
• Exp 1
• Exp 2
• Exp 3
• Exp 4
• Exp 5
• Exp 6
• Exp 7
• Exp 8
• Exp 9
• Exp 10
• Exp 11
• Exp 12
• Exp 13
• Exp 14
• Exp 15
• Exp 16
• Exp 17
• Z Power 1
• Z Power 2
• Z Power 3

Important: Many of these equations have a Bailout property on the Properties page found under the equation. If Bailout is present, it must be set to a number less than or equal to 128 for this example.

Experiment 3

For the Angle Relief y2 example, you can change the Fractal Equation to one of several different equations. To do this, select the Fractal Equation: Trig 13 properties page:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Trig 13

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

• NanoGeometry 2
• NanoGeometry 3
• NanoGeometry 6
• NanoGeometry 7
• Pinwheels
• Trig 1
• Trig 10
• Trig 12
• Trig 13
• Trig 14
• Airfoil 2
• Airfoil 3

Experiment 4

Change how coloring is applied to the resulting image.

To do this for the Angle Relief x2 example, select the color controller's Properties page:

General
    Mandelbrot / Julia / Newton
        Classic
            Controllers
                Gradient Map - Angle Relief (x^2)
                    Properties

To do this for the Angle Relief y2 example, select the color controller's Properties page:

General
    Mandelbrot / Julia / Newton
        Classic
            Controllers
                Gradient Map - Angle Relief (y^2)
                    Properties

Change any of the properties on this page to affect how the data is mapped to the gradient.

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

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.