Abrupt Behaviour Changes in Cellular Automata under Asynchronous Dynamics

Abstract

We propose an analysis of the relaxation time of the elementary finite cellular automaton 214 (Wolfram coding) under αasynchronous dynamics (i.e. each cell independently updates with probability 0 < α 6 1 at each time step). While cellular automata have been intensively studied under synchronous dynamics (all cells update at each time step), much less work is available about asynchronous dynamics. In particular, the robustness to asynchronism is a feature which is far from being cleared up. [1,2] have studied double quiescent automata (DQECA) under fully and α-asynchronous dynamics. [1] did not analyse the behavior of all DQECAs and left some conjectures concerning four automata, among which automaton 214 which seems to have a specific behavior under α-synchronous dynamics. Our work partially answers one of those conjectures, and both illustrates the richness of the behaviours involved by asynchronism on cellular automata and the challenge of their mathematical prediction. Far from being a marginal case study, our analysis provides a very relevant example of the way the dynamics is affected by asynchronism and of the mathematical tools which can be used to predict the asymptotic behaviour of such complex systems.

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Cite this paper

@inproceedings{Regnault2006AbruptBC, title={Abrupt Behaviour Changes in Cellular Automata under Asynchronous Dynamics}, author={Damien Regnault}, year={2006} }