Algorithmic mapping from criticality to self-organized criticality

Probabilistic cellular automata are prototypes of nonequilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany-Kinzel model) and the dynamical Ising model. The critical properties of these models are usually obtained by fine tuning one or more control parameters as, for instance, the temperature. We present a method for the parallel evolution of the model for all the values of the control parameter, although its implementation is in general limited to a fixed number of values. This algorithm facilitates the sketching of phase diagrams and can be useful in deriving the critical properties of the model. Since the criticality here emerges from the asymptotic distribution of some quantities, without tuning of parameters, our method is a mapping from a probabilistic cellular automaton with critical behavior to a self-organized critical model with the same critical properties.