Phase Transitions in Two-Dimensional Kauffman Cellular Automata
Bernard Derrida, Dietrich Stauffer · Europhysics Letters (EPL) · 1986
In the random Boolean networks suggested by Kauffman, each site is changed to random rules depending on neighbours of this site. One can define two kinds of models, the annealed for which the random rules are changed at each time step, and the quenched for which the random rules remain fixed. We consider this model mostly on a square lattice with nearest-neighbour interactions. In the annealed case the phase transition observed in the overlap of configurations differing in the initial conditions is related to directed percolation on the body-centred cubic lattice; in the quenched case, the original Kauffman model, the phase transition is seen in the variation of this final overlap with the initial overlap.