Equivalence of Cellular Automata to Ising Models and Directed Percolation

Abstract

Time development of cellular automata in $d$ dimensions is mapped onto equilibrium statistical mechanics of Ising models in $d+1\mathrm{}$ dimensions. Directed percolation is equivalent to a cellular automaton, and thus to an Ising model. For a particular case of directed percolation we find ${\nu }_{\parallel }=2\mathrm{}$, ${\nu }_{\perp }=1\mathrm{}$, ${\eta }_{\perp }=0\mathrm{}$.