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International Conference on Numerical Analysis and Its Applications

NAA 2008: Numerical Analysis and Its Applications pp 168–175Cite as

Minimal Simplex for IFS Fractal Sets

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

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.

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Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering and Information Technologies, Ss Cyril and Methodius University, P.O. Box 574, Skopje, Macedonia

    Elena Babače

  2. Faculty of Electronic Engineering, University of Niš, P.O. Box 73, 18 000 Niš, Serbia

    Ljubiša Kocić

Authors
  1. Elena Babače
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  2. Ljubiša Kocić
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

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© 2009 Springer-Verlag Berlin Heidelberg

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Babače, E., Kocić, L. (2009). Minimal Simplex for IFS Fractal Sets. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_16

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  • DOI: https://doi.org/10.1007/978-3-642-00464-3_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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