Orbit Traps - Part 8

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In Part 8 of the tutorial, we will try out the Apollonian Gasket orbit trap.

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.

Leave Max Dwell as 1 in the Orbit Trap Orbit Generation section.

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.

On the program's Properties page, set Index Map to Trap Index.

This will use the sample's Trap Index to index into the list of gradients.

Next, select the Instructions: Circle properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                Instructions: Circle

This page is a Program Editor for the Orbit Trap.

Change the Based On property to Apollonian Gasket.

Select the program's Properties page.

The 1st example will use the default Layout of 1 ring of N tangent circles plus unit circle.

Set the Depth to 32, Radius Cutoff to 0.002, and Min Radius to 0.002.

Finally, set Scale to 1.8.

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

Apollonian Gasket (Orbit Trap)

Next, change Layout to 2 rings of N tangent circles.

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

Apollonian Gasket (Orbit Trap)

Next, change Layout to 2 rings of N tangent circles plus unit circle.

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

Apollonian Gasket (Orbit Trap)

Now, reset Layout to 1 ring of N tangent circles plus unit circle.

Set N to 6 and set Scale back to 1.

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

Apollonian Gasket (Orbit Trap)

Note that the radius of the entire image is 1.0 and the radius of the inner circle is 1/3 (0.33333...).

Next, select the Transformation properties page:

General
    Mandelbrot / Julia / Newton
        Transformation

This page allows you to maintain a list of Transformations used to transform the pixel prior to starting each orbit. The transformations are applied in series to the pixel value; i.e., the point resulting from each transformation is passed to the next transformation in the list. As you will see, this can have a dramatic effect on the resulting image. By default, there is a single transformation, Identity, and the Identity transformation does not alter the input point.

For this tutorial, we will use a single transformation.

Next, select the Identity properties page:

General
    Mandelbrot / Julia / Newton
        Transformation
            Identity

This page is a Program Editor for the Transformation.

Change the Based On property to Droste Effect - Circles.

Read the comments in the program's Instructions at the bottom of the page and then select the program's Properties page just below the transformation in the hierarchy.

Set the Inner Radius to 0.33333 and the Outer Radius to 1.

This transformation maps the part of the image found between the 2 circles defined by Inner Radius and Outer Radius, onto the entire complex plane.

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

Apollonian Gasket (Orbit Trap)

You can also use the Orbit Trap Controller Pattern Map - Texture.

This controller is used to map Textures onto the trap's surface. I do not include any textures with the product so you will need to find some on the Internet to try this controller out. There are many textures available on the Internet. Try searching for seamless textures as a starting point.

A good source for seamless textures is Genetica Viewer by Spiral Graphics. Genetica Viewer is a free application for rendering seamless textures that were created in Genetica. I highly recommend that you download Genetica Viewer. The download includes hundreds of seamless textures plus editing functionality to generate countless different variations of each texture.

There is also a nice set of public domain textures found at Public Domain Textures.

If you do not have access to any textures at this time, skip the remainder of this part of the tutorial.

Add 7 textures to the controller's Texture List Control as we did in Part 5 of the tutorial, and on the program's Properties page, set Index Map to Trap Index as shown below.

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

Apollonian Gasket (Orbit Trap)

Finding a good set of textures that work together is a challenge but the results are worth it.

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