Cell-centric heuristics for the classification of cellular automata

Abstract

We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two novel entropy measures, one that is also based on inputs to the cells, the other based on state transitions by the cells. Our two new entropies are both targeted at the classification of update rules by parallel machines, being therefore mindful of the necessary communications requirements; we call them cell-centric input entropy and cell-centric transition entropy to reflect this fact. We report on extensive computational experiments on both one- and two-dimensional cellular automata. These experiments allow us to conclude that the two new entropies possess strong discriminatory capabilities, therefore providing valuable aid in the classification process.