Set manipulations of fractal objects using matrices of IFS

  • Joélle Thollot
From Principles to Application
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)

Abstract

One of the major problems in geometric modeling is the control of shape construction. Indeed, one should be able to construct geometrical forms by combining or manipulating simple entities. This problem is even more important when we deal with fractal geometry. In this paper, we propose some methods for increasing the modeling capabilities of fractal shape constructions. We propose an extension of the IFS model based on the definition of matrices of IFS that provides a constructive approach of fractal shapes.

Key words

Fractals geometric modeling IFS matrices of IFS 

References

  1. [Bar88]
    M.F. Barnsley. Fractals Everywhere. Academic press, INC, 1988.Google Scholar
  2. [BM89]
    J. Berstel and M. Morcrette. Compact representation of patterns by finite automata. In Proceedings of Pixim, pages 387–395, 1989.Google Scholar
  3. [CD93]
    K. Culik II and S. Dube. Rationnal and affine expressions for image synthesis. Discrete Appl. Math., 41:85–120, 1993.Google Scholar
  4. [DTG95]
    S. Duval, M. Tagine, and D. Ghazanfarpour. Modélisation de fractals par les arbres étiquetés. In 3emes journées AFIG, Marseille, pages 125–134, novembre 1995.Google Scholar
  5. [Gen92]
    C. Gentil. Les Fractales en Synthèse d'Images: le Modèle IFS. PhD thesis, Université Claude Bernard LYON 1, France, 1992.Google Scholar
  6. [PH91]
    P. Prusinkiewicz and M.S. Hammel. Automata, languages and iterated function systems. In lecture notes for the SIGGRAPH'91 course: “Fractal modeling in 3D computer graphics and imagery”, 1991.Google Scholar
  7. [PH92]
    P. Prusinkiewicz and M.S. Hammel. Escape-time visualization method for language-restricted iterated function systems. In Proceedings of Graphics Interface'92, May 1992.Google Scholar
  8. [PJS92]
    H.O. Peitgen, H. Jürgens, and D. Saupe. Encoding images by simple transformations. In Fractals For The Classroom, New York, 1992.Google Scholar
  9. [Tho96]
    J. Thollot. Extension du Modèle IFS pour une Géométrie Fractale Constructive. PhD thesis, Université Claude Bernard LYON 1, France, sept 1996.Google Scholar
  10. [TT93]
    J. Thollot and E. Tosan. Construction of fractales using formal languages and matrices of attractors. In Harold P. Santos, editor, Proceedings of Compugraphics'93, pages 74–81, Technical University of Lisbon, december 1993.Google Scholar
  11. [TT95]
    J. Thollot and E. Tosan. Constructive fractal geometry: constructive approach to fractal modeling using languages operations. In Proceedings of Graphics Interface'95, Quebec, Canada, pages 196–203, may 1995.Google Scholar
  12. [ZT96]
    C. Zair and E. Tosan. Fractal modeling using free forms techniques. In Proceedings of Eurographics, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Joélle Thollot
    • 1
    • 2
  1. 1.LIGIM - Bât 710 - Université Claude BernardVILLEURBANNE Cedex
  2. 2.Laboratoire d'Informatique Graphique Image et ModélisationItaly

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