Observation of novel patterns in a stressed lattice-gas model of swarming

This paper intends to revisit the behaviour of a lattice-gas cellular automaton model of swarming, in which particles are oriented according to an interaction rule that favours local alignment. This model has been shown to display a phase transition between an ordered and a disordered phase in a parametrical plane of the particle density and alignment sensitivity. We "stress" this model by setting extreme values for these parameters and observe the emergence of novel organised patterns which, surprisingly, do not necessarily maximise the global motion of particles. We show that even with the model being stochastic and simple, the self-organisation process can result in a variety of behaviours. We discuss these observations in the light of the study of discretisation effects.

[1]  A. Schadschneider,et al.  Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics , 2004 .

[2]  Vicsek,et al.  Lattice-gas model for collective biological motion. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[4]  Cristian Spitoni,et al.  Metastability for Reversible Probabilistic Cellular Automata with Self-Interaction , 2007 .

[5]  Andreas Deutsch,et al.  A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms , 2008, 0806.2475.

[6]  Ali A Minai,et al.  Phase transition in a swarm algorithm for self-organized construction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Raissa M D'Souza,et al.  Coexisting phases and lattice dependence of a cellular automaton model for traffic flow. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Dani Lischinski,et al.  Crowds by Example , 2007, Comput. Graph. Forum.

[9]  Hiroaki Kitano,et al.  Biological robustness , 2008, Nature Reviews Genetics.

[10]  B. Chopard,et al.  Lattice-Gas Cellular Automaton Models for Biology: From Fluids to Cells , 2010, Acta biotheoretica.

[11]  H. Bussemaker,et al.  Mean-Field Analysis of a Dynamical Phase Transition in a Cellular Automaton Model for Collective Motion , 1997, physics/9706008.

[12]  S. Whitelam,et al.  The role of collective motion in examples of coarsening and self-assembly. , 2008, Soft matter.

[13]  D. Helbing,et al.  Lattice gas simulation of experimentally studied evacuation dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1998 .

[15]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[16]  Luís Correia,et al.  Effects of asynchronism on evolutionary games. , 2011, Journal of theoretical biology.

[17]  Andreas Deutsch,et al.  Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion , 2010, Comput. Math. Appl..