1+1D directed percolation on a spacetime lattice. Activity spreads forward in time with probability p. At p_c ≈ 0.6447 the system undergoes a continuous phase transition.
Directed Percolation is the canonical universality class for absorbing state transitions. The order parameter is the density of active sites ρ.
Near p_c: ρ ~ (p-p_c)^β, β≈0.2765 (1+1D)
Correlation length: ξ_⊥ ~ |p-p_c|^(-ν_⊥), ν_⊥≈1.097
Temporal: ξ_∥ ~ |p-p_c|^(-ν_∥), ν_∥≈1.734
Active (white) → can infect neighbors in next time step. Absorbing state (black) = no activity, no escape.