J. Harmen, A. Bussemaker, E. Deutsch, and . Geigant, Meanfield analysis of a dynamical phase transition in a cellular automaton model for collective motion, Physical Review Letters, vol.78, issue.26, pp.5018-5021, 1997.

[. Bouré, N. Fatès, and V. Chevrier, First steps on asynchronous lattice-gas models with an application to a swarming rule, Natural Computing, vol.410, issue.47???49, pp.551-560, 2013.
DOI : 10.1007/s11047-013-9389-2

[. Bouré, N. Fatès, and V. Chevrier, A Robustness Approach to Study Metastable Behaviours in a Lattice-Gas Model of Swarming, Proceedings of Automata'13
DOI : 10.1007/978-3-642-40867-0_6

A. Barberousse and C. Imbert, New mathematics for old physics: The case of lattice fluids. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, pp.231-241, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01098484

A. Deutsch and S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation ? Characterization, Applications, and Analysis. Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, 2005.

A. Deutsch, ORIENTATION-INDUCED PATTERN FORMATION: SWARM DYNAMICS IN A LATTICE-GAS AUTOMATON MODEL, International Journal of Bifurcation and Chaos, vol.06, issue.09, pp.61735-1752, 1996.
DOI : 10.1142/S0218127496001077

[. Fatès, A Guided Tour of Asynchronous Cellular Automata, Journal of Cellular Automata, vol.9, issue.56, pp.387-416, 2014.
DOI : 10.1007/978-3-642-40867-0_2

I. Marcovici, Automates cellulaires probabilistes et mesures spécifiques sur des espaces symbolique

J. Mairesse and I. Marcovici, Around probabilistic cellular automata, Theoretical Computer Science, vol.559, pp.42-72, 2014.
DOI : 10.1016/j.tcs.2014.09.009
URL : https://hal.archives-ouvertes.fr/hal-01194762

[. Regnault, N. Schabanel, and E. Thierry, Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority, Theoretical Computer Science, vol.410, pp.47-494844, 2009.

L. Taggi, Critical Probabilities and Convergence Time of Percolation Probabilistic Cellular Automata, Journal of Statistical Physics, vol.9, issue.176, pp.853-892, 2015.
DOI : 10.1007/s10955-015-1199-8

L. and {. .. X}-×-{0, (i, j) ? L, i = 0 or i = X ? 1 or j = 0 or, ) ? L, i = 0}. By noting the initial condition x ? Q L for each (i, j) ? L, taking x

J. ). Etc, We call this last set of 4 conditions, the integrity condition. The integrity condition guarantees that no particle will travel to a border cell (in B) It is easy to see that the propagation step preserves the integrity condition, but not the interaction step. Our method thus consists in checking if the north channel of a cell of B N is occupied. In this case, the particle is re-affected among the free channels of the cell, with a uniform probability. All happens as if the particle has " bounced " on a northern wall. Clearly, such a rearrangement is always possible as this cell can not contain four particles, The same procedures is applied for the three other directions