Topological classification of cellular automata
Philippe M. Binder · Journal of Physics A Mathematical and General · 1991
The author summarizes an extensive numerical study of basin and attractor sizes among the 88 distinct elementary cellular automata (CA) rules. Based on this study and on previous work in discretized dynamical systems, he proposes a new classification of CA, complementary to that of Wolfram, in which attractor globality is important. With the use of fixed boundary conditions he finds global periodic attractors in CA for the first time. Not a single instance of attractor chaos is observed in this class of rules.