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International Conference on Parallel Computing Technologies

PaCT 2013: Parallel Computing Technologies pp 330–343Cite as

Parallel Implementation of Totalistic Cellular Automata Model of Stable Patterns Formation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7979))

Abstract

Totalistic cellular automata (TCA) with weighted templates simulating pattern formation process are investigated. The investigation aims to create a method for porous media morphology synthesis according to a given set of properties such as porosity, percolation, density, etc. The proposed method is based on a parallel composition of TCA and an asynchronous CA (CA of second layer), whose evolution allows to obtain a set of patterns representing different porous media morphologies. Implementation of three-dimensional version of the CA-model is performed by means of block-synchronous transformation. Plausibility of the transformation is shown by comparison of simulation results. In addition, estimates of TCA with second layer parallel implementation efficiency is presented.

Supported by (1) Presidium of Russian Academy of Sciences, Basic Research Program N 15.9-5 (2012), (2) Grant RFBR 11-01-00567a, (3) Siberian Branch of Russian Academy of Sciences, SBRAS Interdisciplinary Project 47.

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References

  1. Turing, A.M.: The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 237(641), 37–72 (1952)

    Article  Google Scholar 

  2. Zhabotinskiy, A.M., Zaikin, A.N.: Concentration wave propogation in a two-dimensional, liquid phase self-oscillating system. Nature 225, 535 (1970) (in Russian)

    Google Scholar 

  3. Young, D.A.: A local activator-inhibitor model of vertebrate skin patterns. Theory and applications of cellular automata. Advanced series on complex systems, vol. 1, pp. 320–327. World Scientific Publishing Co. Pte. Ltd. (1986)

    Google Scholar 

  4. Vanag, V.K.: Dissociative structures in reaction-diffusion systems, p. 300. Institute of computer researches, Regular and chaotic dynamics, Izhevsk (2008) (in Russian)

    Google Scholar 

  5. Wolfram, S.: A New Kind of Science. Wolfram Media (2002)

    Google Scholar 

  6. Wolfram, S.: Cellular Automata as Simple Self-Organizing Systems. Caltech preprint CALT-68-938 (1982), http://www.stephenwolfram.com/publications/articles/ca/82-cellular/index.html

  7. Chua, L.O.: CNN: a paradigm for complexity. Series on nonlinear science. Series A, vol. 31, p. 320. World Scientific Publishing Co. Pte. Ltd., Singapore (1998)

    MATH  Google Scholar 

  8. Bandman, O.: Using Cellular Automata for porous media simulation. The Journal of Supercomputing 57(2), 121–131 (2011)

    Article  Google Scholar 

  9. Bandman, O.: Parallel simulation of asynchronous cellular automata evolution. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 41–47. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Nedea, S.V., Lukkien, J.J., Hilbers, P.A.J., Jansen, A.P.J.: Methods for parallel simulations of surface reactions. Advances in Computation: Theory and Practice, Parallel and Distributed Scientific and Engineering Computing 15, 85–97 (2004)

    Google Scholar 

  11. Kalgin, K.V.: Similarity of the evolutions of cellular automaton in asynchronous and block-synchronous modes. In: New Information Technologies in the Study of Complex Structures: Proceedings of the 9-th Russian Conference, p. 21. NTL, Tomsk (2012) (in Russian)

    Google Scholar 

  12. Achasova, S., Bandman, O., Markova, V., Piskunov, S.: Parallel Substitution Algorithm. Theory and Application. World Scientific Publishing Co. Pte. Ltd., Singapore (1994)

    Book  MATH  Google Scholar 

  13. Sharifulina, A.: Investigation of Stable Patterns Formed by Totalistic Cellular Automata Evolution. In: Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2012. LNCS, vol. 7495, pp. 161–170. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  14. Bandman, O.: Using multi core computers for implementing cellular automata systems. In: Malyshkin, V. (ed.) PaCT 2011. LNCS, vol. 6873, pp. 140–151. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Sharifulina, A., Elokhin, V.: Simulation of Heterogeneous Catalytic Reaction by Asynchronous Cellular Automata on Multicomputer. In: Malyshkin, V. (ed.) PaCT 2011. LNCS, vol. 6873, pp. 204–209. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Ivchenko, G.I., Medvedev, Y.I.: Introduction to mathematical statistics. Moscow - LKI. P. 600 (2010) (in Russian)

    Google Scholar 

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Author information

Authors and Affiliations

  1. ICM&MG SB RAS, Pr. Lavrentjeva, 6, Novosibirsk, Russia

    Anastasiya Kireeva

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  1. Anastasiya Kireeva
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Editors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Supercomputer Department, Russian Academy of Science, 630090, Novosibirsk, Russia

    Victor Malyshkin

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Kireeva, A. (2013). Parallel Implementation of Totalistic Cellular Automata Model of Stable Patterns Formation. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2013. Lecture Notes in Computer Science, vol 7979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39958-9_31

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  • DOI: https://doi.org/10.1007/978-3-642-39958-9_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39957-2

  • Online ISBN: 978-3-642-39958-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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