Equivalence of Cellular Automata to Ising Models and Directed Percolation
Eytan Domany, Wolfgang Kinzel · Physical Review Letters · 1984
Time development of cellular automata in $d$ dimensions is mapped onto equilibrium statistical mechanics of Ising models in $d+1$ dimensions. Directed percolation is equivalent to a cellular automaton, and thus to an Ising model. For a particular case of directed percolation we find ${\ensuremath{ u}}_{\ensuremath{\parallel}}=2$, ${\ensuremath{ u}}_{\ensuremath{\perp}}=1$, ${\ensuremath{\eta}}_{\ensuremath{\perp}}=0$.