Parallel computation of fractal sets with the help of neural networks and cellular automata

  • Vasily Severyanov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1277)


Fractal sets of a broad class are described by Deterministic Iterated Function Systems. It has been shown by J. Stark that one can build a binary asymmetric Neural Network whose attractor gives an approximation of the corresponding fractal set. The author of the article has suggested a version of the Neural Network Algorithm which is more convenient and efficient in some cases. Here we show a way of going from Deterministic Iterated Function Systems to a special class of Cellular Automata and give a hint how our Neural Network Algorithm can be converted to become a Cellular Automaton Algorithm. Cellular automata are simpler than neural networks and well suited for parallel implementation.


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  1. 1.
    Achasova, S., Bandman, O.: Correctness of Parallel Computation Processes. Nauka, Novosibirsk, 1990, 252 p., in RussianGoogle Scholar
  2. 2.
    Bandman, O.: Cellular-Neural Computations. Formal Model and Possible Applications. In: Lecture Notes in Computer Science 964 (1995) 21Google Scholar
  3. 3.
    Toffoli, T., and Margolus, N.: Cellular Automaton Machines: a New Environment for Modeling. MIT press, 1997Google Scholar
  4. 4.
    Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman and Co., San Francisco, 1982Google Scholar
  5. 5.
    Barnsley, M. F.: Fractals Everywhere. Springer-Verlag, Berlin, 1986Google Scholar
  6. 6.
    Stark,J.: Neural Networks 4 (1991) 679Google Scholar
  7. 7.
    Bressloff, P. C., and Stark, J.: Neural Networks, Learning Automata and Iterated Function Systems. In: Fractals and Chaos, ed. A. J. Crilly, R. A. Earnshow, H. Jones et al., Springer-Verlag, New-York, 1991, 145Google Scholar
  8. 8.
    Rumelhart, D. E., Hinton, G. E., and Williams, R. J.: Parallel Distributed Processing. MIT Press, Cambridge, 1986Google Scholar
  9. 9.
    Humpert, B.: Comp. Phys. Comm. 58 (1990) 223Google Scholar
  10. 10.
    Severyanov, V. M.: Calculation and Interactive Construction of Flat Fractals Using Neural Networks. In: New Computing Techniques in Physics Research IV, Proc. IV Int. Workshop on Software Engineering and Artificial Intelligence for High Energy and Nuclear Physics, Pisa, Italy, 3–8 April, 1995, ed. B. Denby, D. Perret-Gallix, Word Scientific, Singapore, 1995, 509Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vasily Severyanov
    • 1
  1. 1.Joint Institute for Nuclear ResearchDubna, Moscow regionRussia

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