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

Authors:
Nazim Fatès;Lucas Gerin
Affiliations:
INRIA Nancy Grand-Est --- LORIA --- MaIA team,;IECN - Univ. Nancy I,
Venue:
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
Year:
2008

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Abstract

We study the convergence properties of cellular automata under fully asynchronous updating, i.e., when a single cell is selected at random at each time unit. We tackle this question for the two-dimensional totalistic cellular automata. As a first step for studying this class, we focus on a few examples that are, in our view, representative of the diversity of the behaviours found in dimension two. The richness of the evolutions we consider underlines that the updating scheme plays a central role in the evolution of a cellular automaton.