Table of Contents Author Guidelines Submit a Manuscript
Volume 2017 (2017), Article ID 1280351, 8 pages
Research Article

An Information-Based Classification of Elementary Cellular Automata

1Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, USA
2ASU-SFI Center for Biosocial Complex Systems, Arizona State University, Tempe, AZ, USA
3School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA
4Blue Marble Space Institute of Science, Seattle, WA, USA

Correspondence should be addressed to Enrico Borriello

Received 7 March 2017; Revised 11 June 2017; Accepted 27 July 2017; Published 7 September 2017

Academic Editor: Sergio Gómez

Copyright © 2017 Enrico Borriello and Sara Imari Walker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.