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Some counterintuitive non-monotonicities in probabilistic rules in the Game of Life
Konstantin Storozhuk1, Vadim Pashinin2
1Institute of Mathematics SB RAS, Prospekt Akademika Koptyuga, 4, Novosibirsk, Novosibirsk Oblast, Russia, 630090. stork931@gmail.com.
Abstract:
We investigate and partially explain some of the ≪counterintuitive≫ effects that arise in a probabilistic analogue of Conway's ≪life≫ cellular automaton when cells are allowed to come to life or die out with certain probabilities depending on the number of living neighbors. Some biological analogies turned out to be appropriate. One of the most intriguing observations: if we add to the standard ≪B3S23≫ rules of the ≪Game of Life≫ cellular automaton a stochastic rule whereby a dead cell is born with five neighbors with probability p, then for [Formula: see text] this leads to an increase in population compared to the standard rules, while for [Formula: see text] it leads to degradation.
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