<p>We investigate and partially explain some of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ll \)</EquationSource> </InlineEquation>counterintuitive<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gg \)</EquationSource> </InlineEquation> effects that arise in a probabilistic analogue of Conway’s <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ll \)</EquationSource> </InlineEquation>life<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\gg \)</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\ll \)</EquationSource> </InlineEquation>B3S23<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\gg \)</EquationSource> </InlineEquation> rules of the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\ll \)</EquationSource> </InlineEquation>Game of Life<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\gg \)</EquationSource> </InlineEquation> cellular automaton a stochastic rule whereby a dead cell is born with five neighbors with probability <i>p</i>, then for <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(0&lt; p &lt; 0.09\)</EquationSource> </InlineEquation> this leads to an increase in population compared to the standard rules, while for <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(p &gt; 0.1\)</EquationSource> </InlineEquation> it leads to degradation.</p>

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Some counterintuitive non-monotonicities in probabilistic rules in the Game of Life

  • Konstantin Storozhuk,
  • Vadim Pashinin

摘要

We investigate and partially explain some of the \(\ll \) counterintuitive \(\gg \) effects that arise in a probabilistic analogue of Conway’s \(\ll \) life \(\gg \) 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 \(\ll \) B3S23 \(\gg \) rules of the \(\ll \) Game of Life \(\gg \) cellular automaton a stochastic rule whereby a dead cell is born with five neighbors with probability p, then for \(0< p < 0.09\) this leads to an increase in population compared to the standard rules, while for \(p > 0.1\) it leads to degradation.