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Generating Maximal Domino Patterns by Cellular Automata Agents

  • Rolf Hoffmann
  • Dominique DésérableEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10421)

Abstract

Considered is a 2D cellular automaton with moving agents. The objective is to find agents controlled by a Finite State Program (FSP) that can form domino patterns. The quality of a formed pattern is measured by the degree of order computed by counting matching \(3 \times 3\) patterns (templates). The class of domino patterns is defined by four templates. An agent reacts on its own color, the color in front, and whether it is blocked or not. It can change the color, move or not, and turn into any direction. Four FSP were evolved for multi-agent systems with 1, 2, 4 agents initially placed in the corners of the field. For a \(12 \times 12\) training field the aimed pattern could be formed with a 100% degree of order. The performance was also high with other field sizes. Livelocks are avoided by using three different variants of the evolved FSP. The degree of order usually fluctuates after reaching a certain threshold, but it can also be stable, and the agents may show the termination by running in a cycle, or by stopping their activity.

Keywords

Cellular automata agents Multi-agent system Pattern formation Evolving FSM behavior Spatial computing 

References

  1. 1.
    Shi, D., He, P., Lian, J., Chaud, X., Bud’ko, S.L., Beaugnon, E., Wang, L.M., Ewing, R.C., Tournier, R.: Magnetic alignment of carbon nanofibers in polymer composites and anisotropy of mechanical properties. J. App. Phys. 97, 064312 (2005)CrossRefGoogle Scholar
  2. 2.
    Itoh, M., Takahira, M., Yatagai, T.: Spatial arrangement of small particles by imaging laser trapping system. Opt. Rev. 5(1), 55–58 (1998)CrossRefGoogle Scholar
  3. 3.
    Jiang, Y., Narushima, T., Okamoto, H.: Nonlinear optical effects in trapping nanoparticles with femtosecond pulses. Nat. Phys. 6, 1005–1009 (2010)CrossRefGoogle Scholar
  4. 4.
    Niss, M.: History of the Lenz-Ising model, 1920–1950: from ferromagnetic to cooperative phenomena. Arch. Hist. Exact Sci. 59(3), 267–318 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Press, D., Ladd, T.D., Zhang, B., Yamamoto, Y.: Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218–221 (2008)CrossRefGoogle Scholar
  6. 6.
    Bagnold, R.E.: The Physics of Blown Sand and Desert Dunes. Chapmann and Hall, Methuen, London (1941)Google Scholar
  7. 7.
    Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. B237, 37–72 (1952)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Tyson, J.J.: The Belousov-Zhabotinskii Reaction. Lecture Notes in Biomathematics. Springer, Heidelberg (1976). doi: 10.1007/978-3-642-93046-1 CrossRefzbMATHGoogle Scholar
  9. 9.
    Greenberg, J.M., Hastings, S.P.: Spatial patterns for discrete models of diffusion in excitable media. SIAM J. Appl. Math. 34(3), 515–523 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Progogine, I., Stengers, I.: Order out of Chaos. Heinemann, London (1983)Google Scholar
  11. 11.
    Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)CrossRefzbMATHGoogle Scholar
  12. 12.
    Deutsch, A., Dormann, S.: Cellular Automaton Modeling of Biological Pattern Formation. Birkäuser, Boston (2005)zbMATHGoogle Scholar
  13. 13.
    Désérable, D., Dupont, P., Hellou, M., Kamali-Bernard, S.: Cellular automata in complex matter. Complex Syst. 20(1), 67–91 (2011)MathSciNetGoogle Scholar
  14. 14.
    Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55(3), 601–644 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    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). doi: 10.1007/978-3-540-73849-7_31 CrossRefGoogle Scholar
  16. 16.
    Yamins, D., Nagpal, R., Automated global-to-local programming in 1-D spatial multi-agent systems. In: Proceedings of the 7th International Conference on AAMAS, pp. 615–622 (2008)Google Scholar
  17. 17.
    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). doi: 10.1007/978-3-319-11520-7_70 Google Scholar
  18. 18.
    Hoffmann, R.: Cellular automata agents form path patterns effectively. Acta Phys. Pol. B Proc. Suppl. 9(1), 63–75 (2016)CrossRefGoogle Scholar
  19. 19.
    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). doi: 10.1007/978-3-319-44365-2_42 CrossRefGoogle Scholar
  20. 20.
    Birgin, E.G., Lobato, R.D., Morabito, R.: An effective recursive partitioning approach for the packing of identical rectangles in a rectangle. J. Oper. Res. Soc. 61, 303–320 (2010)CrossRefzbMATHGoogle Scholar
  21. 21.
    Bonabeau, E.: From classical models of morphogenesis to agent-based models of pattern formation. Artif. Life 3(3), 191–211 (1997)CrossRefGoogle Scholar
  22. 22.
    Hamann, H., Schmickl, T., Crailsheim, K.: Self-organized pattern formation in a swarm system as a transient phenomenon of non-linear dynamics. Math. Comput. Mod. Dyn. Syst. 18(1), 39–50 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Bandini, S., Vanneschi, L., Wuensche, A., Shehata, A.B.: A neuro-genetic framework for pattern recognition in complex systems. Fundam. Inf. 87(2), 207–226 (2008)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Halbach, M., Hoffmann, R., Both, L.: Optimal 6-state algorithms for the behavior of several moving creatures. In: Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 571–581. Springer, Heidelberg (2006). doi: 10.1007/11861201_66 CrossRefGoogle Scholar
  25. 25.
    Ediger, P., Hoffmann, R.: Optimizing the creature’s rule for all-to-all communication. In: Adamatzky, A., et al. (eds.) Automata 2008, pp. 398–412 (2008)Google Scholar
  26. 26.
    Ediger, P., Hoffmann, R.: Solving all-to-all communication with CA agents more effectively with flags. In: Malyshkin, V. (ed.) PaCT 2009. LNCS, vol. 5698, pp. 182–193. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-03275-2_19 CrossRefGoogle Scholar
  27. 27.
    Hoffmann, R., Désérable, D.: All-to-all communication with cellular automata agents in 2\(D\) grids. J. Supercomput. 69(1), 70–80 (2014)CrossRefGoogle Scholar
  28. 28.
    Ediger, P., Hoffmann, R.: CA models for target searching agents. Elec. Notes Theor. Comput. Sci. 252, 41–54 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Ediger, P., Hoffmann, R., Désérable, D.: Routing in the triangular grid with evolved agents. J. Cell. Autom. 7(1), 47–65 (2012)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Ediger, P., Hoffmann, R., Désérable, D.: Rectangular vs triangular routing with evolved agents. J. Cell. Autom. 8(1–2), 73–89 (2013)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Komann, M., Mainka, A., Fey, D.: Comparison of evolving uniform, non-uniform cellular automaton, and genetic programming for centroid detection with hardware agents. In: Malyshkin, V. (ed.) PaCT 2007. LNCS, vol. 4671, pp. 432–441. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-73940-1_43 CrossRefGoogle Scholar
  32. 32.
    Mesot, B., Sanchez, E., Peña, C.-A., Perez-Uribe, A.: SOS++: finding smart behaviors using learning and evolution. In: Artificial Life VIII, pp. 264–273. MIT Press (2002)Google Scholar
  33. 33.
    Blum, M., Sakoda, W.J.: On the capability of finite automata in 2 and 3 dimensional space. In: SFCS 1977, pp. 147–161 (1977)Google Scholar
  34. 34.
    Rosenberg, A.L.: Algorithmic insights into finite-state robots. In: Sirakoulis, G., Adamatzky, A. (eds.) Robots and Lattice Automata. Emergence, Complexity and Computation, vol. 13, pp. 1–31. Springer, Cham (2015). doi: 10.1007/978-3-319-10924-4_1 Google Scholar
  35. 35.
    Hoffmann, R.: The GCA-w massively parallel model. In: Malyshkin, V. (ed.) PaCT 2009. LNCS, vol. 5698, pp. 194–206. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-03275-2_20 CrossRefGoogle Scholar
  36. 36.
    Hoffmann, R.: Rotor-routing algorithms described by CA-w. Acta Phys. Pol. B Proc. Suppl. 5(1), 53–67 (2012)CrossRefGoogle Scholar
  37. 37.
    Hoffmann, R., Désérable, D.: Routing by cellular automata agents in the triangular lattice. In: Sirakoulis, G., Adamatzky, A. (eds.) Robots and Lattice Automata. Emergence, Complexity and Computation, vol. 13, pp. 117–147. Springer, Cham (2015). doi: 10.1007/978-3-319-10924-4_6 Google Scholar
  38. 38.
    Lahlouhi, A.: MAS-td: an approach to termination detection of multi-agent systems. In: Gelbukh, A., Espinoza, F.C., Galicia-Haro, S.N. (eds.) MICAI 2014. LNCS, vol. 8856, pp. 472–482. Springer, Cham (2014). doi: 10.1007/978-3-319-13647-9_42 Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Technische Universität DarmstadtDarmstadtGermany
  2. 2.Institut National des Sciences Appliquées, RennesRennesFrance

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