Robustness of cellular automata in the light of asynchronous information transmission

Abstract

Cellular automata are classically synchronous: all cells are simultaneously updated. However, it has been proved that perturbations in the updating scheme may induce qualitative changes of behaviours. This paper presents a new type of asynchronism, the β-synchronism, where the transmission of information between cells is disrupted randomly. After giving a formal definition, we experimentally study the behaviour of β-synchronous models. We observe that, although many effects are similar to those induced by the perturbation of the update, novel phenomena occur. We study the qualitative variation of behaviour triggered by continuous change of the disruption probability. In particular we observe that phase transitions appear, which belong to the directed percolation universality class. © 2011 Springer-Verlag Berlin Heidelberg.