eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2011-01-01
DMTCS Proceedings vol. AP,...
Proceedings
10.46298/dmtcs.2972
2972
journal article
Orbits of the Bernoulli measure in single-transition asynchronous cellular automata
Henryk FukÅ›
Andrew Skelton
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.
https://dmtcs.episciences.org/2972/pdf
cellular automata. asynchronous rules
measure dynamics
[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]