Symmetric Icon

The Symmetric Icon example displays a symmetric icon but rather than tracking the orbit point as is normally the case, we track a triangle metric point instead. That is, as the orbit progresses, we use the last 3 orbit points to define a triangle, compute a triangle metric point based on the triangle, and accumulate statistics into the triangle metric point rather than the original orbit point as is normally done. For any given symmetric icon attractor, we can produce many different variations simply by varying the triangle metric calculation (see Experiment 2).

Experiment 1

Change the base attractor that defines the symmetric icon. To do this, select the equation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Orbital Equation: Symmetric Icon - Standard Formula
            Properties

Change the Icon property to select 1 of the attractors. Do not change the remaining properties on this page since it is unlikely your change will produce a fractal. All of the attractors in this list were found using the program Symmetric Icon - Standard Formula (Search) which generates sets of values that meet a set of user-defined criteria. Try that program out later when you have time.

Experiment 2

Change the triangle metric point used to define the point into which we accumulate statistics. To do this, select the Triangle Metric properties page:

General
    Triangle Metric

Change the Triangle Metric property in the p1 section. The other properties on this page also affect the resulting triangle metric point. When you have time, read the Triangle Metric page documentation for details. For now, ignore these other properties.

Experiment 3

Change the transformation applied to the base fractal before the symmetry transformation. To do this, select the transformation's Properties page:

General
    Orbital / IFS / Strange Attractor
        Transformation 1
            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.

Experiment 4

Change the color blend used to color the image. To do this, select the color controller's Properties page:

General
    Orbital / IFS / Strange Attractor
        Controllers
            Direct Color Map - RGB Blend
                Properties

Change the Blend Type to any of the supported color blends.