Combined Effect of Topology and Synchronism Perturbation on Cellular Automata: Preliminary Results

  • Jean-Baptiste Rouquier
  • Michel Morvan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5191)


The aim of this paper is to experimentally study the combined effect of the introduction of two kinds of structural perturbations to the behavior of cellular automata. We present the results obtained by simultaneously perturbing synchronism and topology of elementary cellular automata. We show that very interesting and different behaviors appear, including phase transitions and non monotonicity (i.e. introduction of both perturbations is less effective than the introduction of only one of them). These results lead us to think that this study is worth to be now developed more accurately.


Phase Transition Cellular Automaton Cellular Automaton Order Phase Transition Universality Class 
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  1. 1.
    Fatès, N., Morvan, M.: An experimental study of robustness to asynchronism for elementary cellular automata. Complex Systems 16, 1–27 (2005)MathSciNetGoogle Scholar
  2. 2.
    Ingerson, T.E., Buvel, R.L.: Structure in asynchronous cellular automata. Physica D Nonlinear Phenomena 10, 59–68 (1984)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Fatès, N.: Asynchronism induces second order phase transitions in elementary cellular automata. Journal of Cellular Automata (March 2007)Google Scholar
  4. 4.
    Rouquier, J.B., Morvan, M.: Coalescing cellular automata: Synchronization by common random source for asynchronous updating. Journal of Cellular Automata (accepted, 2008)Google Scholar
  5. 5.
    Schönfisch, B., de Roos, A.: Synchronous and asynchronous updating in cellular automata. Biosystems 51(3), 123–143 (1999)CrossRefGoogle Scholar
  6. 6.
    Fatès, N., Morvan, M.: Perturbing the topology of the game of life increases its robustness to asynchrony. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 111–120. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Fatès, N., Morvan, M., Schabanel, N., Thierry, E.: Fully asynchronous behavior of double-quiescent elementary cellular automata. Theoretical Computer Science 362, 1–16 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Fatès, N.: Experimental study of elementary cellular automata dynamics using the density parameter. In: Discrete models for complex systems, DMCS 2003 (Lyon). Discrete Mathematics Theoretical Computer Science Proceedings, AB, Nancy. Assoc. Discrete Math. Theor. Comput. Sci, pp. 155–165 (2003)Google Scholar
  9. 9.
    Grassberger, P.: Are damage spreading transitions generically in the universality class of directed percolation? J. Stat. Phys. 79, 13–23 (1995)zbMATHCrossRefGoogle Scholar
  10. 10.
    Hinrichsen, H.: Nonequilibrium critical phenomena and phase transitions into absorbing states. Advances in Physics 7, 815–958 (2000)CrossRefGoogle Scholar
  11. 11.
    Fatès, N.: Robustesse de la dynamique des systèmes discrets: le cas de l’asynchronisme dans les automates cellulaires. PhD thesis, ENS Lyon (December 2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jean-Baptiste Rouquier
    • 1
  • Michel Morvan
    • 1
    • 2
  1. 1.Université de Lyon, IXXI and ENS LyonFrance
  2. 2.EHESS and Santa Fe Institute 

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