L-System Fractals - Part 2

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In Part 2 of the tutorial, we are going to create an L-System orbit trap. The advantage of using an orbit trap is that we have access to the rich set of orbit trap related methods to transform/alter the image. In fact, that is the subject of Part 3 and Part 4, but first we need to create the L-System orbit trap.

Execute the Reset to Defaults command on the File menu of the Fractal Window and select the Mandelbrot / Julia / Newton properties page:

General
    Mandelbrot / Julia / Newton

We are going to define an L-System orbit trap so we need to set Type to Orbit Trap in the Mandelbrot / Julia/ Newton section of the page.

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 L-System 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 L-System.

Next, select the L-System properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                L-System

We are going to use one of the L-System fractals defined in the default L-System file Examples.l so we do not need to change the L-System File property. Change the other properties to match what is shown below; i.e., set Radius to 1.5, Order to 5, and Line Width to 0.05.

Next, select the L-System Instructions properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Orbit Trap Map
                L-System
                    L-System Instructions

Set L-System to Hilbert as we did in Part 1.

Next, select the Controllers properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Controllers

This page allows you to maintain the list of Color Controllers used to map the sample data to specific colors for display. Typically, you will only use a single controller and will not need to make any changes on this page.

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.

Orbit Trap Controllers are programs (called controllers hereafter) that map sample data collected during the fractal iteration, to colors for display. Each controller is composed of a set of properties and Instructions. The properties are in a set of sections at the top of the page and the instructions are at the bottom of the page. To view the instructions, use the editor's Toggle Code View button to hide the properties and expand the instructions to fill the space. See Toolbar Buttons for details.

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 L-System a stone-like appearance.

Next, select the program's Properties page:

General
    Mandelbrot / Julia / Newton
        Orbit Trap
            Controllers
                Pattern Map - Perlin Noise
                    Properties

At the top of the page in the General Options section, change Factor to 1.

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

L-System Fractal (Orbit Trap)

Note that for the images included in Part 3 and Part 4, I also changed Gradient Offset to vary the color of the fractal. Gradient Offset is an offset into the controller's list of gradients, and I used values 0 through 5 to vary the color. Leave the value at 0 for now and return to this page at any time if you want to change the color. Simply set the Gradient Offset to a value from 0 to 5 and execute the Display Fractal command on the Tools menu of the Fractal Window to generate the fractal image.

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