Thermodynamics and Complexity of Cellular Automata
R. Badii, Antonio Politi · Physical Review Letters · 1997
The complexity exhibited by cellular automata is studied using both topological (graph-theoretical) and metric (thermodynamic) techniques. A novel topological classification, based on a hierarchy of languages, is introduced. In particular, it is shown that the elementary rule 22 is able to produce, upon iteration, a deep nesting of grammatical rules and that this asymptotically yields a phase transition when the thermodynamic formalism is applied to the limit spatial configuration.