Demonstration of density classification by two 2D probabilistic cellular automata
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Fukś, Henryk
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Abstract
Demonstration of the solution of the density classification problem for initial density 0.501, performed by a pair of 2D cellular automaton rules described in H. Fukś, "Solving two-dimensional density classification problem with two probabilistic cellular automata", Journal of Cellular Automata, 10(1--2):149--160, 2015 (also availabe at https://arxiv.org/abs/1506.06653). The rules used are generalized ECA 184 with random "lane changes" and generalized ECA 232 with random "crowd avoidance".
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Video file with resolution 418x416, 1 min 10 sec duration. Black sites represent 0, blue represent 1. Initial configuration is 100x100 with density 0.501, meaning that there are 5100 sites in state 1 and 4900 in state 0. Periodic boundary conditions are used.
The rule changes after 1000 iterations (approx. in 42 sec.) , and at the end all sites are blue (in state 1), as expected for the initial density > 0.5.
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