An Information-Based Classification of Elementary Cellular Automata

• Main Authors: Enrico Borriello, Sara Imari Walker
• Format: Article
• Language: English
• Published: Hindawi-Wiley 2017-01-01
• Series: Complexity
• Online Access: http://dx.doi.org/10.1155/2017/1280351

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.