Kolmogorov complexity and cellular automata classification

AbstractWe present a new approach to cellular automata (CA) classification based on algorithmic complexity. We construct a parameter κ which is based only on the transition table of CA and measures the “randomness” of evolutions; κ is better, in a certain sense, than any other parameter recursively definable on CA tables. We investigate the relations between the classical topological approach and ours. Our parameter is compared with Langton's λ parameter: κ turns out to be theoretically better and also agrees with some practical evidences reported in literature. Finally, we propose a protocol to approximate κ and make experiments on CA dynamical behavior