Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems

This article studies the convergence properties of some 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.

• Type: Conference
• Year: 2008
• Where: ACRI
• Authors: Nazim Fatès, Lucas Gerin
• Keywords: ACRI 2008, Artificial Intelligence, Cellular Automata, Convergence Properties, Nearest Neighbours