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Diploid Cellular Automata: First Experiments on the Random Mixtures of Two Elementary Rules

  • Nazim FatèsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10248)

Abstract

We study a small part of the 8088 diploid cellular automata. These rules are obtained with a random mixture of two deterministic Elementary Cellular Automata. We use numerical simulations to study the mixtures obtained with three blind rules: the null rule, the identity rule and the inversion rule. As the mathematical analysis of such systems is a difficult task, we use numerical simulations to get insights into the dynamics of this class of stochastic cellular automata. We are particularly interested in studying phase transitions and various types of symmetry breaking.

Keywords

Stochastic cellular automata Probabilistic cellular automata Symmetry breaking Synchronisation 

References

  1. 1.
    Arrighi, P., Schabanel, N., Theyssier, G.: Stochastic cellular automata: correlations, decidability and simulations. Fundamenta Informaticae 126(2–3), 121–156 (2013)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bołt, W., Baetens, J.M., De Baets, B.: On the decomposition of stochastic cellular automata. J. Comput. Sci. 11, 245–257 (2015). arXiv:1503.03318
  3. 3.
    Dennunzio, A., Formenti, E., Manzoni, L., Mauri, G.: m-asynchronous cellular automata: from fairness to quasi-fairness. Nat. Comput. 12(4), 561–572 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dennunzio, A., Formenti, E., Manzoni, L., Mauri, G., Porreca, A.E.: Computational complexity of finite asynchronous cellular automata. Theoret. Comput. Sci. 664, 131–143 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fatès, N.: Stochastic cellular automata solutions to the density classification problem - when randomness helps computing. Theory Comput. Syst. 53(2), 223–242 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fatès, N.: A guided tour of asynchronous cellular automata. J. Cell. Automata 9(5–6), 387–416 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Fatès, N.: Remarks on the cellular automaton global synchronisation problem. In: Kari, J. (ed.) AUTOMATA 2015. LNCS, vol. 9099, pp. 113–126. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-47221-7_9 CrossRefGoogle Scholar
  8. 8.
    Mairesse, J., Marcovici, I.: Around probabilistic cellular automata. Theor. Comput. Sci. 559, 42–72 (2014). Non-uniform Cellular AutomataGoogle Scholar
  9. 9.
    Ricardo, J., Mendonça, G., de Mário, J., de Oliveira, M.J.: An extinction-survival-type phase transition in the probabilistic cellular automaton p182–q200. J. Phys. A Math. Theor. 44(15), 155001 (2011)CrossRefGoogle Scholar
  10. 10.
    Regnault, D.: Proof of a phase transition in probabilistic cellular automata. In: Béal, M.-P., Carton, O. (eds.) DLT 2013. LNCS, vol. 7907, pp. 433–444. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38771-5_38 CrossRefGoogle Scholar
  11. 11.
    Richard, G.: On the synchronisation problem over cellular automata. To appear, Private communication (2017)Google Scholar
  12. 12.
    Schüle, M., Stoop, R.: A full computation-relevant topological dynamics classification of elementary cellular automata. Chaos 22(4), 043143 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Silva, F., Correia, L., Christensen, A.L.: Modelling synchronisation in multirobot systems with cellular automata: analysis of update methods and topology perturbations. In: Sirakoulis, G.C., Adamatzky, A. (eds.) Robots and Lattice Automata. ECC, vol. 13, pp. 267–293. Springer, Cham (2015). doi: 10.1007/978-3-319-10924-4_12 Google Scholar
  14. 14.
    Taggi, L.: Critical probabilities and convergence time of percolation probabilistic cellular automata. J. Stat. Phys. 159(4), 853–892 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Turing, A.: The chemical basis of morphogenesis. Philos. Trans. Royal Soc. (London) 237, 5–72 (1952)MathSciNetCrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.Inria Nancy – Grand Est; LORIA UMR 7503Villers-lès-NancyFrance

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