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.