An Information-Based Classification of Elementary Cellular Automata
Enrico Borriello, Sara Imari Walker · Complexity · 2017
We propose a novel, information-based classification of elementary cellular automata. The classification scheme proposed circumvents the problems associated with isolating whether complexity is in fact intrinsic to a dynamical rule, or if it arises merely as a product of a complex initial state. Transfer entropy variations processed by cellular automata split the 256 elementary rules into threeinformation classes, based on sensitivity to initial conditions. These classes form a hierarchy such that coarse-graining transitions observed among elementary rules predominately occur within each information-based class or, much more rarely, down the hierarchy.