Neighbourhood 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 neighbourhood detection algorithm which can determine the range of the neighbourhood without any knowledge of the system by introducing a criterion based on Mutual Information (MI) 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.