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  1. Home > Articles & Issues >
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  3. Orbits of the Bernou ...
Conference paper

Orbits of the Bernoulli measure in single-transition asynchronous cellular automata

Henryk Fukś ORCID (1), Andrew Skelton (1)
(1) Department of Mathematics and Statistics [St. Catharines]
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Imported on
January 31, 2017
Published on
December 31, 2010
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
Proceedings
DOI
10.46298/dmtcs.2972
License
https://about.hal.science/hal-authorisation-v1
Natural Sciences and Engineering Research Council of Canada
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Orbits of the Bernoulli measure in single-transition asynchronous cellular automata

Henryk Fukś ORCID (1), Andrew Skelton (1)
(1) Department of Mathematics and Statistics [St. Catharines]
Abstract
We study iterations of the Bernoulli measure under nearest-neighbour asynchronous binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicitly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions for probabilities of ones for all three minimal single-transition rules, as well as expressions for probabilities of blocks of length 3 for some of them. These expressions can be interpreted as "response curves'', that is, curves describing the dependence of the final density of ones on the initial density of ones.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
  • [NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • cellular automata. asynchronous rules
  • measure dynamics
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