Subcritical monotone cellular automata
Paul Balister, Béla Bollobás, Robert Morris, Paul Smith
Abstract
Abstract We study monotone cellular automata (also known as ‐bootstrap percolation) in with random initial configurations. Confirming a conjecture of Balister, Bollobás, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non‐zero for all subcritical models.
Topics & Concepts
Cellular automatonMonotone polygonConjectureMathematicsPercolation (cognitive psychology)Zero (linguistics)Discrete mathematicsAutomatonCombinatoricsStatistical physicsComputer scienceTheoretical computer scienceAlgorithmPhysicsGeometryNeuroscienceLinguisticsPhilosophyBiologyStochastic processes and statistical mechanicsCellular Automata and ApplicationsMarkov Chains and Monte Carlo Methods