Eden Growth Model

The Eden growth model adds cells randomly to the perimeter of a growing cluster — mimicking bacterial colony growth or tumor expansion. Despite its simplicity, the surface belongs to the KPZ universality class (Kardar-Parisi-Zhang 1986), with roughness exponent β≈1/3. The KPZ equation ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η describes surface growth with nonlinear tilt-dependent velocity. The 1D KPZ fluctuations follow the Tracy-Widom distribution (GUE), connecting surface growth to random matrix theory.