PHASE-TRANSITIONS IN AN ELEMENTARY PROBABILISTIC CELLULAR-AUTOMATON

Cellular automata exhibit a large variety of dynamical behaviors, from fixed-point convergence and periodic motion to spatio-temporal chaos. By introducing probabilistic interactions, and regarding the asymptot ic density Phi of non-quiescent cell states as an order parameter, pha se transitions may be identified from a quiescent phase with Phi=0 to a chaotic phase with non-zero Phi. We consider an elementary one-dimen sional probabilistic cellular automaton (PCA) with deterministic limit s given by the quiescent rule 0, the rule 72 that evolves into a non-t rivial fixed point, and the chaotic rules 18 and 90. Despite the simpl icity of the rules, the PCA shows a surprising number of transition ph enomena. We identify 'second-order' phase transitions from Phi=0 to Ph i > 0 with static and dynamic exponents that differ from those of dire cted percolation. Moreover, we find that the non-trivial fixed-point r ule 72 is a singular point in PCA space.