Minimal Simplex for IFS Fractal Sets

Abstract

Fractal sets manipulation and modeling is a difficult task due to their complexity and unpredictability. One of the basic problems is to determine bounds of a fractal set given by some recursive definitions, for example by an Iterated Function System (IFS). Here we propose a method of bounding an IFS-generated fractal set by a minimal simplex that is affinely identical to the standard simplex. First, it will be proved that for a given IFS attractor, such simplex exists and it is unique. Such simplex is then used for definition of an Affine invariant Iterated Function System (AIFS) that then can be used for affine transformation of a given fractal set and for its modeling.KeywordsConvex HullIterate Function SystemNonempty Compact SubsetStandard SimplexStandard Orthonormal BasisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.