DIRECTED-PERCOLATION CONJECTURE FOR CELLULAR-AUTOMATA

The directed-percolation (DP) hypothesis for stochastic, range-4 cellu lar automata with an acceptance rule y less than or equal to Sigma(j = -4)(4) s(i - j), in the cases of y : {1,...,5}, S-i:{0, 1} was invest igated in one and two dimensions. Simulations, as well as mean-field r enormalization-group and coherent-anomaly calculations, show that in o ne dimension the phase transitions for y < 4 are continuous and belong to the DP class, while for y = 4, 5 they are discontinuous. The same rules in two dimensions for y = 1 show (2 + 1)-dimensional DP universa lity; but in the cases of y > 1 the transitions become first order.