Cluster growth in the KPZ universality class: interface width w ~ t^β, β ≈ 1/3
Growing...
Grid width140
Noise η0.50
Growth speed8
The Eden model grows a cluster by randomly adding sites adjacent to the cluster boundary.
The resulting rough interface belongs to the KPZ universality class (Kardar-Parisi-Zhang).
Interface width: w(t) = √(⟨h²⟩ − ⟨h⟩²) ~ t^β with β ≈ 1/3 (KPZ in 1+1D).
The KPZ class is characterized by exponents α=1/2, β=1/3, z=3/2 relating roughness, growth, and dynamic scaling.
Log-log plot of w vs t shown right — slope approaches 1/3 (green dashed line).