Identification of the neighborhood and CA rules from spatio-temporal CA patterns

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually produces a CA rule table without providing a clear understanding of the structure of the neighborhood or the CA rule. In this paper, a new identification method based on using a modified orthogonal least squares or CA-OLS algorithm to detect the neighborhood structure and the underlying polynomial form of the CA rules is proposed. The Quine-McCluskey method is then applied to extract minimum Boolean expressions from the polynomials. Spatio-temporal patterns produced by the evolution of one-dimensional (1-D), two-dimensional (2-D), and higher dimensional binary CAs are used to illustrate the new algorithm and simulation results show that the CA-OLS algorithm can quickly select both the correct neighborhood structure and the corresponding rule.