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Perturbing the Topology of the Game of Life Increases Its Robustness to Asynchrony

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3305))

Abstract

An experimental analysis of the asynchronous version of the “Game of Life” is performed to estimate how topology perturbations modify its evolution. We focus on the study of a phase transition from an “inactive-sparse phase” to a “labyrinth phase” and produce experimental data to quantify these changes as a function of the density of the initial configuration, the value of the synchrony rate, and the topology missing-link rate. An interpretation of the experimental results is given using the hypothesis that initial “germs” colonize the whole lattice and the validity of this hypothesis is tested.

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References

  1. Bagnoli, F., Rechtman, R., Ruffo, S.: Some facts of life. Physica A 171, 249–264 (1991)

    Article  MathSciNet  Google Scholar 

  2. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning ways for your mathematical plays, ch. 25, vol. 2. Academic Press, London (1982) ISBN 0-12-091152-3

    Google Scholar 

  3. Bersini, H., Detours, V.: Asynchrony induces stability in cellular automata based models. In: Brooks, R.A., Maes, Pattie (eds.): Proceedings of the 4th International Workshop on the Synthesis and Simulation of Living Systems Artif icialLifeIV, pp. 382–387. MIT Press, Cambridge (1994)

    Google Scholar 

  4. Blok, H.J., Bergersen, B.: Effect of boundary conditions on scaling in the game of Life. Physical Review E 55, 6249–6252 (1997)

    Article  Google Scholar 

  5. Blok, H.J., Bergersen, B.: Synchronous versus asynchronous updating in the game of life. Phys. Rev. E 59, 3876–3879 (1999)

    Article  Google Scholar 

  6. Buvel, R.L., Ingerson, T.E.: Structure in asynchronous cellular automata. Physica D 1, 59–68 (1984)

    MathSciNet  Google Scholar 

  7. Fatès, N.: Experimental study of elementary cellular automata dynamics using the density parameter. Discrete Mathematics and Theoretical Computer Science Proceedings AB, 155–166 (2003)

    Google Scholar 

  8. Fatès, N., Morvan, M.: An experimental study of robustness to asynchronism for elementary cellular automata, arxiv:nlin.CG/0402016 (submitted 2004)

    Google Scholar 

  9. Huang, S.-Y., Zou, X.-W., Tan, Z.-J., Jin, Z.-Z.: Network-induced nonequilibrium phase transition in the game of life. Physical Review E 67 (2003) 026107

    Google Scholar 

  10. Huberman, B.A., Glance, N.: Evolutionary games and computer simulations. Proceedings of the National Academy of Sciences, USA 90, 7716–7718 (1993)

    Article  MATH  Google Scholar 

  11. Illachinski, A.: Cellular automata - a discrete universe. World Scientific, Singapore (2001)

    Google Scholar 

  12. Packard, N.H., Wolfram, S.: Two-dimensional cellular automata. Journal of Statistical Physics 38, 901–946 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  13. Poundstone, W.: The recursive universe. William Morrow and Company, New York (1985) ISBN 0-688-03975-8

    Google Scholar 

  14. Schönfisch, B., de Roos, A.: Synchronous and asynchronous updating in cellular automata. BioSystems 51, 123–143 (1999)

    Article  Google Scholar 

  15. Serra, R., Villani, M.: Perturbing the regular topology of cellular automata: Implications for the dynamics. In: Proceedings of the 5th International Conference on Cellular Automata for Research and Industry (Geneva), pp. 168–177 (2002)

    Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Fatès, N., Morvan, M. (2004). Perturbing the Topology of the Game of Life Increases Its Robustness to Asynchrony. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_12

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  • DOI: https://doi.org/10.1007/978-3-540-30479-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23596-5

  • Online ISBN: 978-3-540-30479-1

  • eBook Packages: Springer Book Archive

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