
Journal for Geometry and Graphics 16 (2012), No. 2, 129137 Copyright Heldermann Verlag 2012 General Rules of Fractals Construction from Polyhedra Andrzej Katunin Institute of Fundamentals of Machinery Design, Silesian University of Technology, Konarskiego 18A, 44100 Gliwice, Poland andrzej.katunin@polsl.pl Dariusz Kurzyk Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44100 Gliwice, Poland dariusz.kurzyk@polsl.pl The paper presents a method of construction of deterministic fractals based on uniform polyhedra using a contraction mapping procedure and an iterated function system algorithm. It was shown that the contraction mapping procedure, which implies the construction of fractals with nonoverlapped and nondisjointed contractions, could produce only a limited number of fractals from uniform polyhedra, which is resulted by geometric specificity of some uniform polyhedra. The lists of uniform polyhedra from which fractals either can be constructed and not were presented and discussed. The contraction ratios and fractal dimensions of the constructed fractals were determined, some of uniform polyhedrabased fractals were presented graphically. Keywords: Fractals, uniform polyhedra, iterated function systems, contraction mapping. MSC: 51M20; 28A80 [ Fulltextpdf (451 KB)] for subscribers only. 