The one-dimensional exactly 1 cellular automaton: replication, periodicity, and chaos from finite seeds

DOI10.1007/s10955-010-0103-9zbMath1222.82034OpenAlexW2121150382MaRDI QIDQ625524

David Griffeath, Janko Gravner

Publication date: 17 February 2011

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-010-0103-9

zbMATH Keywords

entropychaoscellular automatonreplicatorperiodic attractoradditive dynamics

Mathematics Subject Classification ID

Cellular automata (computational aspects) (68Q80) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (8)

Stability of cellular automata trajectories revisited: branching walks and Lyapunov profiles ⋮ Robust periodic solutions and evolution from seeds in one-dimensional edge cellular automata ⋮ Unnamed Item ⋮ Self-Replicating Patterns in 2D Linear Cellular Automata ⋮ Replication in one-dimensional cellular automata ⋮ The Transition Rules of 2D Linear Cellular Automata Over Ternary Field and Self-Replicating Patterns ⋮ Three-state von Neumann cellular automata and pattern generation ⋮ Percolation and disorder-resistance in cellular automata

Uses Software

• Golly

Cites Work

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• Additive one-dimensional cellular automata are chaotic according to Devaney's definition of chaos
• Cellular automaton growth on \(\mathbb{Z}^2\): Theorems, examples, and problems
• The kink of cellular automaton Rule 18 performs a random walk
• Long-range correlations in chaotic cellular automata
• Exact solvability and quasiperiodicity of one-dimensional cellular automata
• Asymptotic densities for PackardBoxrules
• Statistical mechanics of cellular automata
• Complex Systems: Chaos and Beyond
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