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. 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 { f i : X → X   |   1 ≤ i ≤ N } {displaystyle {f_{i}:X o X | 1leq ileq N}} be an iterated function system, or a set of contractions from a compact set X {displaystyle X} to itself. The operator H {displaystyle H} is defined over subsets S ⊂ X {displaystyle Ssubset X} as A key question is to describe the attractors A = H ( A ) {displaystyle A=H(A)} of this operator, which are compact sets. One way of generating such a set is to start with an initial compact set S 0 ⊂ X {displaystyle S_{0}subset X} (which can be a single point, called a seed) and iterate H {displaystyle H} as follows