Symmetry Transformation

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Symmetry Transformation Properties Page

The Fractal Science Kit fractal generator Symmetry Transformation page is used to define a symmetry transformation. A symmetry transformation is used to transform an orbit point into multiple points. In addition, the symmetry transformation associates each output point with a symmetry index that can be used by the Color Controllers to color the point. Despite the name, the symmetry transformation need not produce a symmetric design. Many of the built-in symmetry transformations do produce symmetric designs but a Symmetry Transformation can be used whenever a 1-to-many transformation is required.

The Symmetry Transformation page is found in 2 places. First, it is found under the Orbit Trap page. The symmetry transformation is applied to the orbit point prior to orbit trap processing and each of the resulting points is passed to the orbit trap, which can result in up to N trapped points, where N is the number of points returned by the symmetry transformation.

Second, the Symmetry Transformation page is found under the Orbital / IFS / Strange Attractor page. The symmetry transformation is applied to the orbit point prior to accumulating the orbit point data into the sample data and each of the returned points is passed to the accumulation process which can result in modifying up to N sample points, where N is the number of points returned by the symmetry transformation.

In both locations, the Symmetry Transformation page is sandwiched between Transformation 1 and Transformation 2. Transformation 1 is a transformation applied to the orbit point prior to passing it to the symmetry transformation. Transformation 2 is a transformation applied to each of the points that result from applying the symmetry transformation. This organization allows a great deal of flexibility.

The Symmetry Transformation page is a Program Editor for a Symmetry Transformation. This is a special transformation that maps a single input point to 0 or more output points that defines the symmetry. Each output point is a SymmetryTransformationInfo object which contains a Point and an Index. The Point is the transformed point and the Index is the associated symmetry index.

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