The Eden model simulates bacterial colony growth: start with a seed, then at each step randomly choose a perimeter site and fill it. The growing interface belongs to the Kardar-Parisi-Zhang (KPZ) universality class.
KPZ scaling: interface width W(t) ~ tβ with β ≈ 1/3. The saturated roughness scales as W ~ Lα with α ≈ 1/2 (in 1+1D). The dynamic exponent is z = α/β ≈ 3/2. These exponents are exact and universal — the same appear in random matrix theory (Tracy-Widom distribution).
The roughness plot shows W(t) vs. time on a log-log scale. The slope estimates β in real time.