Multivalued fractals

Multivalued fractals are considered as fixed-points of certain induced union operators, called the Hutchinson–Barnsley operators, in hyperspaces of compact subsets of the original spaces endowed with the Hausdorff metric. Various approaches are presented for obtaining the existence results, jointly with the information concerning the topological structure of the set of multivalued fractals. According to the applied fixed-point principles, we distinguish among metric, topological and Tarski’s multivalued fractals. Finite families of condensing and (locally) compact maps as well as of different sorts of contractions are examined with this respect. In particular, continuation principle for multivalued fractals is established for (locally) compact maps. Multivalued fractals are also generated implicitly by means of differential inclusions. A randomization of the deterministic results is indicated. Numerical aspects of computer generated multivalued fractals are discussed in detail.