Orbit Traps - Part 6

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In Part 6 of the tutorial, we are going to use a different Fractal Equation as the basis for the orbit trap and generate several Julia fractals.

Execute the Reset to Defaults command on the File menu of the Fractal Window.

Select the Mandelbrot / Julia / Newton properties page:

General
    Mandelbrot / Julia / Newton

Set Type to Orbit Trap in the Mandelbrot / Julia/ Newton section of the page.

Set Max Dwell to 100 in the Orbit Trap Orbit Generation section.

Next, select the Orbit Trap Map properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map

At the top of the page is the list of active orbit traps.

By default, a single orbit trap is defined called Instructions: Circle. We want to use the Circle orbit trap so we need to select the Instructions: Circle item (it is already selected unless you unselected it) and then, in the Selected Orbit Trap Properties section, set Type to Circle.

Next, select the Gradient Map - Value properties page:

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

This page is a Program Editor for the Orbit Trap Controller.

Change the Based On property to Pattern Map - Perlin Noise.

This controller colors the orbit trap by mapping a pattern based on Perlin Noise onto the trap. This will give our trap a stone-like appearance.

Next, scroll down to the 3D Mapping section, and set Peak to Constant (Position: S).

This moves the trap's highlight toward the outside edge of the trap.

On the program's Properties page, set Gradient Count to 2. Note that Gradient Offset determines which 2 gradients to use. The Julia fractals below were generated using Gradient Offset values of 0, 2, 4, 6, 8, and 10.

Next, select the Fractal Equation: Mandelbrot properties page:

General
    Mandelbrot / Julia / Newton
        Fractal Equation: Mandelbrot

This page is a Program Editor for the Fractal Equation.

Change the Based On property to Convergent Map 3.

Execute the Display Fractal command on the Tools menu of the Fractal Window to generate the fractal image.

Orbit Trap (Pattern Map - Perlin Noise)

This is a Mandelbrot fractal and you can view some of the associated Julia fractals by selecting the Preview Julia item on the Tools menu of the Fractal Window.

Once you have selected this item, the Fractal Science Kit changes the cursor to a cross and places the Fractal Window into a state where clicking on the Mandelbrot fractal generates a Julia fractal preview in the Preview Window. The point on the Mandelbrot fractal where you click is used as the Julia Constant for the preview.

Try clicking at various points on the Mandelbrot fractal and view the resulting Julia. If you click on the image in the Preview Window, a new Fractal Window will open with a full-sized version of the preview.

You can also generate Julia fractals by checking the Julia checkbox on the Fractal Equation page and setting the Julia Constant property to a complex number. Note that the Julia Constant property is only visible if the Julia checkbox is checked.

Check the Julia checkbox and then set the Julia Constant to -1.5. Execute the Display Fractal command on the Tools menu of the Fractal Window to generate the fractal image.

A few examples are shown below:

Julia Constant: -1.5

Julia Constant: -1.3

Julia Constant: -0.9

Julia Constant: -0.4

Julia Constant: 0.36

Julia Constant: 0.66

Below each image is the Julia Constant used to produce the image.

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