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Journal for Geometry and Graphics 16 (2012), No. 2, 129--137
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, 44-100 Gliwice, Poland

Dariusz Kurzyk
Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

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 non-overlapped and non-disjointed 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 polyhedra-based fractals were presented graphically.

Keywords: Fractals, uniform polyhedra, iterated function systems, contraction mapping.

MSC: 51M20; 28A80

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