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Critical growth phenomena in cellular automata

✍ Scribed by Kari Eloranta

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
523 KB
Volume
103
Category
Article
ISSN
0167-2789

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✦ Synopsis

We study a one-parameter family of probabilistic cellular automata on square and triangular lattices. Above a critical parameter value a new dominant invariant phase appears resulting in domain growth. In the growth regime a second critical threshold is found above which domains grow at a maximal rate (and facet). This phenomenon is shown to be equivalent to a certain one-dimensional directed percolation problem studied by Domany and Kinzel (1984). Tight bounds are given to the critical probabilities which depend on the lattice. These models are of special interest since their behavior corresponds extremely closely to that of certain simple purely deterministic cellular automata.

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