Symmetric Attractor - Fractal Science Kit Example
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The Symmetric Attractor example displays a symmetric attractor 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 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 attractor. To do this, select the equation's Properties page:
General
Orbital / IFS / Strange
Attractor
Orbital Equation: Symmetric
Attractors
Properties
Change the Item property to select 1 of the attractors. All of the attractors in this list were found using the program Symmetric Attractors (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:
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 color controller used to color the image. To do this, select the color controller's Properties page:
General
Orbital / IFS / Strange
Attractor
Controllers
Gradient Map
- Value
Properties
Changing these properties to control the data to color mapping.
Color Scheme selects which gradient to use.
Try setting the Value property to one of the following values:
- Attractor Index
- Speed
- Acceleration
- Angle
Power, Factor, and Offset control how the value is mapped into the gradient.