Partially permutive cellular automata
@article{Eloranta1993PartiallyPC,
title={Partially permutive cellular automata},
author={Kari Eloranta},
journal={Nonlinearity},
year={1993},
volume={6},
pages={1009-1023}
}One-dimensional cellular automata are analysed via their generalized permutivity. Invariant subalphabets provide a systematic way of identifying periodic and aperiodic tilings as well as stationary distributions invariant under the cellular automaton iteration. In the case of several invariant subalphabets a hierarchy of interaction phenomena arise. In particular the interaction of subalphabets can generate random walks as well as their degenerate forms. A comprehensive scheme emerges that…
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References
SHOWING 1-10 OF 27 REFERENCES
Random walks in cellular automata
- Mathematics, Computer Science
- 1993
Topological defects or phase boundaries discerned in a number of one-dimensional cellular automata appear to perform random walks as well as simpler motions are analyzed to result in a complete classification in the partially permutive case.
Applications of ergodic theory and sofic systems to cellular automata
- Mathematics, Computer Science
- 1984
The kink of cellular automaton rule 18 performs a random walk
- Mathematics
- 1992
We give an exact characterization of the movement of a single kink in the elementary cellular automaton Rule 18. It is a random walk with independent increments as well as independent delay times.…
The Interaction Dynamics of the Kinks in the Cellular Automaton Rule 18
- Computer Science
- 1991
A series of computer simulations on the joint motion of two kinks in the elementary cellular automaton Rule 18 show a remarkably close approximation to the case of independent annihilating random walks except at close range interaction where combinatorial conditions impose an asymmetry on the dynamics.
Particlelike structures and their interactions in spatiotemporal patterns generated by one-dimensional deterministic cellular-automaton rules.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1991
A detailed description of such ``reactions'' sheds new light on the large-time behavior of range-1 Rule 54 with a very slow decrease of the particle number, as ${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensure Math{\gamma}}$ (£0.15).
The attractor—basin portrait of a cellular automaton
- Computer Science
- 1992
The attractor-basin portrait of nonlinear elementary CA rule 18 is described, whose global dynamics is largely determined by a single regular attracting domain, and it is confirmed that in rule 18, isolated dislocation trajectories, as well as a dislocation gas, agree extremely well with the classical model of annihilating diffusive particles.