SIR epidemic spreading on a 2D lattice. Susceptible (dark), Infected (bright), Recovered (dim). Near the critical transmission rate, clusters become fractal — percolation universality class.
The contact process (Harris 1974) is the simplest model exhibiting a non-equilibrium phase transition. At criticality β/γ=1/z (z=4 for square lattice), the infected cluster boundary is a fractal with df≈1.896 — the same as critical percolation (SLE₆).