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An ITERATED FUNCTION SYSTEM (IFS) is a set of CONTRACTIONS, which are ways of scaling the plane by the same amount in every VECTOR BASIS. An ATTRACTOR is the set S (a shape) for which the union of the images of S under the application of all contractions in the given IFS is equivalent to S. A self-similar fractal is then the unique ATTRACTOR of an ITERATED FUNCTION SYSTEM (IFS).
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