A Trade-Off Between Simplicity and Robustness? Illustration on a Lattice-Gas Model of Swarming

  • Nazim FatèsEmail author
  • Vincent Chevrier
  • Olivier Bouré
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)


We re-examine a cellular automaton model of swarm formation. The local rule is stochastic and defined simply as a force that aligns particles with their neighbours. This lattice-gas cellular automaton was proposed by Deutsch to mimic the self-organisation process observed in various natural systems (birds, fishes, bacteria, etc.). We explore the various patterns the self-organisation process may adopt. We observe that, according to the values of the two parameters that define the model, the alignment sensitivity and density of particles, the system may display a great variety of patterns. We analyse this surprising diversity of patterns with numerical simulations. We ask where this richness comes from. Is it an intrinsic characteristic of the model or a mere effect of the modelling simplifications?


  1. 1.
    Barberousse, A., Imbert, C.: New mathematics for old physics: the case of lattice fluids. Stud. Hist. Philos. Sci. Part B: Stud. Hist. Philos. Mod. Phys. 44(3), 231–241 (2013).
  2. 2.
    Bouré, O., Fatès, N., Chevrier, V.: First steps on asynchronous lattice-gas models with an application to a swarming rule. Nat. Comput. 12(4), 551–560 (2013).
  3. 3.
    Bouré, O., Fatès, N., Chevrier, V.: A robustness approach to study metastable behaviours in a lattice-gas model of swarming. In: Kari, J., Kutrib, M., Malcher, A. (eds.) Proceedings of Automata’13. Lecture Notes in Computer Science, vol. 8155, pp. 84–97. Springer, Berlin (2013). (Extended version available as a tech. report at
  4. 4.
    Bussemaker, H.J., Deutsch, A., Geigant, E.: Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion. Phys. Rev. Lett. 78(26), 5018–5021 (1997).
  5. 5.
    Deutsch, A.: Orientation-induced pattern formation: swarm dynamics in a lattice-gas automaton model. Int. J. Bifurc. Chaos 06(09), 1735–1752 (1996).
  6. 6.
    Deutsch, A., Dormann, S.: Cellular Automaton Modeling of Biological Pattern Formation - Characterization, Applications, and Analysis. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Basel (2005)Google Scholar
  7. 7.
    Fatès, N.: FiatLux: a simulation program in Java for cellular automata and discrete dynamical systems available, (Cecill licence) APP IDDN.FR.001.300004.000.S.P.2013.000.10000
  8. 8.
    Fatès, N.: A guided tour of asynchronous cellular automata. J. Cell. Autom. 9(5–6), 387–416 (2014)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Mairesse, J., Marcovici, I.: Around probabilistic cellular automata. Theor. Comput. Sci. 559, 42–72 (2014).
  10. 10.
    Marcovici, I.: Automates cellulaires probabilistes et mesures spécifiques sur des espaces symboliques. Ph.D. thesis, Université Paris 7 (2013). (Text in English)
  11. 11.
    Regnault, D., Schabanel, N., Thierry, E.: Progresses in the analysis of stochastic 2D cellular automata: a study of asynchronous 2D minority. Theor. Comput. Sci. 410(47–49), 4844–4855 (2009).
  12. 12.
    Taggi, L.: Critical probabilities and convergence time of percolation probabilistic cellular automata. J. Stat. Phys. 159(4), 853–892 (2015).

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Nazim Fatès
    • 1
    Email author
  • Vincent Chevrier
    • 2
  • Olivier Bouré
    • 2
  1. 1.inria, Université de Lorraine, CNRS, LORIANancyFrance
  2. 2.Université de Lorraine, CNRS, LORIANancyFrance

Personalised recommendations