Progresses in the Analysis of Stochastic 2D Cellular Automata A Study of Asynchronous 2D Minority 1st Edition by Damien Regnault, Nicolas Schabanel, Eric Thierry ISBN 9783540744566

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ISBN 10: 
ISBN 13: 9783540744566
Author: Damien Regnault, Nicolas Schabanel, Eric Thierry

Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under asynchronous updates. Still, the few mathematical analyses of asynchronism focus on one-dimensional probabilistic cellular automata, either on single examples or on specific classes. As for other classic dynamical systems in physics, extending known methods from one- to two-dimensional systems is a long lasting challenging problem.

In this paper, we address the problem of analysing an apparently simple 2D asynchronous cellular automaton: 2D Minority where each cell, when fired, updates to the minority state of its neighborhood. Our experiments reveal that in spite of its simplicity, the minority rule exhibits a quite complex response to asynchronism. By focusing on the fully asynchronous regime, we are however able to describe completely the asymptotic behavior of this dynamics as long as the initial configuration satisfies some natural constraints. Besides these technical results, we have strong reasons to believe that our techniques relying on defining an energy function from the transition table of the automaton may be extended to the wider class of threshold automata.

Progresses in the Analysis of Stochastic 2D Cellular Automata A Study of Asynchronous 2D Minority 1st Table of contents:

1. Introduction
2. Simulation results
3. Analysis of fully asynchronous 2D Minority
4. Concluding remarks

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