Proper Choice of Spatio-Temporal Scale and Dataset Subsampling for Empirical CA Construction

Here, we consider an appropriate data subsampling procedure for empirical construction of cellular automata (CA). Empirical CA construction is a statistical method to determine a rule of CA by using a given dataset, and this method can be applied to any spatio-temporal datasets in principle. The methodology of constructing the rule was showed by Kawaharada and Iima [5], however it has yet to be developed as a fully convincing method to capture a tendency of space-time patterns of the dataset. In this study, we develop a new procedure to determine the rule by choosing the appropriate spatio-temporal scale to subsample the dataset for more effective empirical CA construction. Using some datasets of numerical solutions of partial differential equations, we illustrate the necessity of the subsampling and elucidate the validity of the new method for the empirical CA construction.