### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 444-447 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 78 |

Issue number | 3 |

Publication status | Published - 20 Jan 1997 |

### Keywords

- DYNAMIC-SYSTEMS
- ATTRACTORS

## Cite this

Badii, R., & Politi, A. (1997). Thermodynamics and complexity of cellular automata.

*Physical Review Letters*,*78*(3), 444-447.