A Study on the Automatic Generation of Asynchronous Cellular Automata Rules by Means of Genetic Algorithms

We present a framework based on genetic algorithms to automatically generate cellular automata rules under four different asynchronous update models (fixed random sweep, random new sweep, clock and independent random ordering). We consider four different rules (18, 56, 110 and 180) with well known dynamics under synchronous update scheme. We try to reconstruct the same dynamics by means of a genetic algorithm using asynchronous update schemes. We show that in many cases it is impossible, by means of an asynchronous update scheme, to perfectly reconstruct these dynamics. Nevertheless, we show that the genetic algorithm finds the rules that more closely approximate the target behavior and the dynamics of the rules found by the genetic algorithm are rather similar to the target ones. In particular, we can always recognize a similar patter and we can also identify some differences in small details, which can be minimal (as for rule 18) or rather visible (as for rule 110). This paves the way to a deeper investigation on this track: does using asynchronous updates allow us to find more stable rules, i.e. rules that are less affected by noise, and thus do not overfit training data? This question remains open and answering it is one of the main goals of our current research.