Complex Transformations

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Symmetry Transformations
Transformations

Complex Transformations Overview

Complex Transformations are instructions used by the Fractal Science Kit fractal generator to transform a complex value into 1 or more other values.

The Fractal Science Kit fractal generator supports 2 different types of Complex Transformations used in different situations for different purposes:

Symmetry Transformations are used to map a single input point to 0 or more output points.

Transformations are used to transform one complex value into another. In some situations, the entire set of orbit points are available to the transformation.

Mandelbrot Fractals and Transformations

When transformations are used with Mandelbrot fractals, the transformation effect could be the opposite of what you might expect. For example, if a 10 degree counter-clockwise rotation is active, the fractal image will be rotated 10 degrees clockwise! If a scaling transformation is active that contracts by 50%, the image will grow by 50%. These differences are due to the nature of Mandelbrot processing with respect to transformations. The pixel is transformed at the beginning of the orbit, and the results are used to color the original (untransformed) pixel. It is as if we transformed the image using the inverse of the transformation that we used to transform the pixel. Orbit Trap processing is affected in the same way.

 

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