Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems
Nazim Fatès and Lucas Gerin
This article studies the convergence properties of some asynchronous 2D cellular automata, when a single cell is updated at random at each time step. We tackle this question for a particular set of rules, namely, the totalistic rules with nearest neighbours. We focus on a few examples that represent, in our view, the diversity of behaviours found in dimension two. These behaviours are analysed quantitatively with an estimation of the time needed to converge to a fixed point.
Keywords: Asynchronous cellular automata, stochastic process, two-dimensional particle systems.