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.
A key question is to describe the attractors of this operator, which are compact sets. One way of generating such a set is to start with an initial compact set (which can be a single point, called a seed) and iterate as follows
and taking the limit, the iteration converges to the attractor
Hutchinson showed in 1981 the existence and uniqueness of the attractor . The proof follows by showing that the Hutchinson operator is contractive on the set of compact subsets of in the Hausdorff distance.
- Hutchinson, John E. (1981). "Fractals and self similarity". Indiana Univ. Math. J. 30 (5): 713–747. doi:10.1512/iumj.1981.30.30055.
- Barnsley, Michael F.; Stephen Demko (1985). "Iterated function systems and the global construction of fractals". Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 399 (1817): 243–275.