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General rules of fractals construction from polyhedra

  • Silesian University of Technology

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The paper presents a method of construction of deterministic frac- tals 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.

Original languageEnglish
Pages (from-to)129-137
Number of pages9
JournalJournal for Geometry and Graphics
Volume16
Issue number2
Publication statusPublished - 2012

Keywords

  • Contraction mapping
  • Fractals
  • Iterated function systems
  • Uniform polyhedra

ASJC Scopus subject areas

  • Applied Psychology
  • Geometry and Topology
  • Applied Mathematics

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