Clustering in the one-dimensional three-color cyclic cellular automaton

DOI10.1214/aop/1176989705zbMath0806.60096OpenAlexW1981821994WikidataQ30047381 ScholiaQ30047381MaRDI QIDQ1201187

Robert Fisch

Publication date: 17 January 1993

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176989705

zbMATH Keywords

cellular automatonparticle systemsclustering propertiesmean cluster sizeinterparticle distance

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (13)

Dynamic of cyclic automata over \(\mathbb Z^2\) ⋮ Limiting behavior of 3-color excitable media on arbitrary graphs ⋮ Persistence of sums of correlated increments and clustering in cellular automata ⋮ Cyclic cellular automata and Greenberg-Hastings models on regular trees ⋮ Exact probabilities and asymptotics for the one-dimensional coalescing ideal gas ⋮ Some rigorous results for the Greenberg-Hastings model ⋮ Asymptotic behaviour of the one-dimensional ``rock-paper-scissors cyclic cellular automaton ⋮ Invertible behavior in elementary cellular automata with memory ⋮ Invariant measures and convergence properties for cellular automaton 184 and related processes ⋮ Clustering in the three and four color cyclic particle systems in one dimension ⋮ Two applications of percolation to cellular automata. ⋮ Ballistic annihilation and deterministic surface growth. ⋮ Cyclic cellular automata and related processes

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