Hutchinson operator

In mathematics, in the study of fractals, a Hutchinson operator is the collective action of a set of contractions, called an iterated function system. The iteration of the operator converges to a unique attractor, which is the often self-similar fixed set of the operator.

Let ${\displaystyle \{f_{i}:X\to X\ |\ 1\leq i\leq N\}}$ be an iterated function system, or a set of contractions from a compact set ${\displaystyle X}$ to itself. The operator ${\displaystyle H}$ is defined over subsets ${\displaystyle S\subset X}$ as

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