Abstract
The objective in this study is to form a domino pattern by Cellular Automata (CA). In a previous work such patterns were formed by CA agents, which were trained with high effort by the aid of Genetic Algorithm. Now two probabilistic CA rules are designed in a methodical way that can perform this task very reliably even for rectangular fields. The first rule evolves stable sub–optimal pattern. The second rule maximizes the overlap between dominoes thereby maximizing the number of dominoes.
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References
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)
Deutsch, A., Dormann, S.: Cellular Automaton Modeling of Biological Pattern Formation. Birkäuser (2005)
Désérable, D., Dupont, P., Hellou, M., Kamali-Bernard, S.: Cellular automata in complex matter. Complex Syst. 20(1), 67–91 (2011)
Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55(3), 601–644 (1983)
Nagpal, R.: Programmable pattern-formation and scale-independence. In: Minai, A.A., Bar-Yam, Y. (eds.) Unifying Themes in Complex Sytems IV, pp. 275–282. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-73849-7_31
Yamins, D., Nagpal, R.: Automated Global-to-Local programming in 1-D spatial multi-agent systems. In: Proceedings 7th International Conference on AAMAS, pp. 615–622 (2008)
Tomassini, M., Venzi, M.: Evolution of asynchronous cellular automata for the density task. In: Guervós, J.J.M., Adamidis, P., Beyer, H.-G., Schwefel, H.-P., Fernández-Villacañas, J.-L., (eds.): Parallel Problem Solving from Nature – PPSN VIIPPSN 2002. LNCS, vol. 2439, pp. 934–943. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45712-7_90
Birgin, E.G., Lobato, R.D., Morabito, R.: An effective recursive partitioning approach for the packing of identical rectangles in a rectangle. J. Oper. Research Soc. 61, 303–320 (2010)
Hoffmann, R.: How agents can form a specific pattern. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2014. LNCS, vol. 8751, pp. 660–669. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11520-7_70
Hoffmann, R.: Cellular automata agents form path patterns effectively. Acta Phys. Pol. B Proc. Suppl. 9(1), 63–75 (2016)
Hoffmann, R., Désérable, D.: Line patterns formed by cellular automata agents. In: El Yacoubi, S., Wąs, J., Bandini, S. (eds.) ACRI 2016. LNCS, vol. 9863, pp. 424–434. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44365-2_42
Hoffmann, R., Désérable, D.: Generating maximal domino patterns by cellular automata agents. In: Malyshkin, V. (ed.) PaCT 2017. LNCS, vol. 10421, pp. 18–31. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62932-2_2
Achasova, S., Bandman, O., Markova, V., Piskunov, S.: Parallel Substitution Algorithm, Theory and Application. World Scientific, Singapore (1994)
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Hoffmann, R., Désérable, D., Seredyński, F. (2019). A Probabilistic Cellular Automata Rule Forming Domino Patterns. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2019. Lecture Notes in Computer Science(), vol 11657. Springer, Cham. https://doi.org/10.1007/978-3-030-25636-4_26
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DOI: https://doi.org/10.1007/978-3-030-25636-4_26
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