An Information-Based Classification of Elementary Cellular Automata

Abstract EN

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 three information 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.