Eden Model & KPZ Growth

Eden (1961): New cells added uniformly to the perimeter → rough interface. Interface width W(t) ~ t^β with β = 1/3 (KPZ universality class). Kardar-Parisi-Zhang (1986): ∂h/∂t = ν∇²h + λ(∇h)² + η(x,t) — roughness exponent α = 1/2 (1D).