Orbit Transformation

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Orbit Transformation Properties Page

The Fractal Science Kit fractal generator Orbit Transformation page is a Transformation Array used to define a transformation based on 1 or more orbit points. A transformation is a mapping on the complex plane that takes a single complex value and maps it to a new complex value that is the result of the transformation.

During the fractal orbit, the Orbit Transformation definition is used to generate a special point called the Orbit Transformation Point. On several pages throughout the application, this point is available as alternative to the orbit point. For example, Orbital fractals support a Point to Track property which can be set to Orbit Point, Orbit Transformation Point, or Triangle Metric Point. Other examples include the Point to Trap property for orbit traps, the Value property associated with several of the built-in Alternate Mapping types (e.g., Exponential Smoothing, Log Smoothing, Minimum Value, Average Value) and more.

In fact, the Transformation Array page maintains a list of Transformations that are applied in series to transform the input point; i.e., the input point is transformed by the 1st transformation in the list and the resulting point is passed to the 2nd transformation, and so on.

Unlike normal Transformations, the Orbit Transformation instructions can access the entire set of orbit points using the Orbit Functions. In truth, Orbital fractals do not have access to the entire orbit but only the last N points, where N is the value of the Orbit Buffer Size property set on the Orbital / IFS / Strange Attractor page.

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