Neighborhood detection using mutual information for the identification of cellular automata

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually requires a priori information about the observed system, but in many applications little information will be known about the pattern. This paper introduces a new neighborhood detection algorithm which can determine the range of the neighborhood without any knowledge of the system by introducing a criterion based on mutual information (and an indication of over-estimation). A coarse-to-fine identification routine is then proposed to determine the CA rule from the observed pattern. Examples, including data from a real experiment, are employed to evaluate the new algorithm.