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International Conference on Parallel Computing Technologies

PaCT 1997: Parallel Computing Technologies pp 109–114Cite as

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

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

Abstract

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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References

  1. Achasova, S., Bandman, O.: Correctness of Parallel Computation Processes. Nauka, Novosibirsk, 1990, 252 p., in Russian

    Google Scholar 

  2. Bandman, O.: Cellular-Neural Computations. Formal Model and Possible Applications. In: Lecture Notes in Computer Science 964 (1995) 21

    Google Scholar 

  3. Toffoli, T., and Margolus, N.: Cellular Automaton Machines: a New Environment for Modeling. MIT press, 1997

    Google Scholar 

  4. Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman and Co., San Francisco, 1982

    Google Scholar 

  5. Barnsley, M. F.: Fractals Everywhere. Springer-Verlag, Berlin, 1986

    Google Scholar 

  6. Stark,J.: Neural Networks 4 (1991) 679

    Google Scholar 

  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, 145

    Google Scholar 

  8. Rumelhart, D. E., Hinton, G. E., and Williams, R. J.: Parallel Distributed Processing. MIT Press, Cambridge, 1986

    Google Scholar 

  9. Humpert, B.: Comp. Phys. Comm. 58 (1990) 223

    Google Scholar 

  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, 509

    Google Scholar 

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Author information

Authors and Affiliations

  1. Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia

    Vasily Severyanov

Authors
  1. Vasily Severyanov
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Victor Malyshkin

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© 1997 Springer-Verlag Berlin Heidelberg

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Severyanov, V. (1997). Parallel computation of fractal sets with the help of neural networks and cellular automata. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1997. Lecture Notes in Computer Science, vol 1277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63371-5_12

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  • DOI: https://doi.org/10.1007/3-540-63371-5_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63371-6

  • Online ISBN: 978-3-540-69525-7

  • eBook Packages: Springer Book Archive

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