Stochastic cellular automata (SCA) with fixed, but randomly chosen, probabilities (spatial disorder) are studied in D dimensions. For zero disorder, the present SCA reduce to directed percolation in (D+1) space-time, but finite spatial disorder is incompatible with the critical exponents of directed percolation. Monte Carlo calculations of the SCA on several disordered structures in D=1 and D=2 yield new universal exponents. I also discuss the phase diagram of ‘‘diluted’’ SCA, which contains a multicritical point and the SCA analog of a ‘‘Griffiths phase’’ with nonexponential relaxation.

• Received 20 February 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.90