## Computation at the onset of chaos (1988)

Venue: | The Santa Fe Institute, Westview |

Citations: | 91 - 15 self |

### BibTeX

@INPROCEEDINGS{Crutchfield88computationat,

author = {James P. Crutchfield and Karl Young},

title = {Computation at the onset of chaos},

booktitle = {The Santa Fe Institute, Westview},

year = {1988},

pages = {223--269},

publisher = {Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For period-doubling and band-merging cascades, we derive expressions for the entropy, the interdependence of-machine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or context-free Chomsky grammar in this case, we give finite descriptions at the higher computational level of context-free Lindenmayer systems. We construct a restricted indexed context-free grammar and its associated one-way nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via