Orbital Fractals - Part 4

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In Part 4 of the tutorial, we are going to use a triangle metric to transform Example 28 from Part 3 of the tutorial.

Select the Orbital / IFS / Strange Attractor properties page:

General
    Orbital / IFS / Strange Attractor

Set the Point to Track property to Triangle Metric Point.

Setting the Point to Track property to Triangle Metric Point transforms the orbit point before we accumulate statistics in the sample. Triangle Metric Point uses 3 orbit points to define a triangle, and transforms the orbit point based on the current triangle metric setting. For example, if Point to Track is set to Triangle Metric Point and the Triangle Metric is set to the CircumCenter of the last 3 orbit points, instead of visiting each orbit point, we find the CircumCenter for the last 3 orbit points and visit that point instead.

Next, select the Triangle Metric properties page:

General
    Triangle Metric

The Triangle Metric page defines a single point (complex value) based on a triangle metric expression. The Triangle Metric page is divided into 4 sections: the Triangle Metric section that defines several properties and a triangle metric expression, and 3 additional sections (p1, p2, p3) that define 3 orbit point triangles, each with an associated triangle metric. By default, the expression returns the single triangle metric defined by the section p1, and p1 uses the last 3 points in the orbit to define the triangle on which the metric is based. Additional values can be defined by partitioning the orbit point triangle into a set of related triangles and using one of these as the basis for computing the triangle metric. See Triangle Metric for details.

For this tutorial, we will set only the Triangle Metric property in section p1 and accept all the remaining defaults.

Set Triangle Metric to ExCenter A and execute the Display Fractal command on the Tools menu of the Fractal Window.

A few examples are shown below:

ExCenter A

ExCenter B

ExCenter C

Below each image is the value of the Triangle Metric property used to create the image.

Try several additional metrics and view the results.

Before we move on, we need to reset the Point to Track property to Orbit Point on the Orbital / IFS / Strange Attractor properties page.

Select the Orbital / IFS / Strange Attractor properties page:

General
    Orbital / IFS / Strange Attractor

Set the Point to Track property to Orbit Point.

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