Diffusion-Limited Aggregation — Witten-Sander

Fractal cluster growth · d_f ≈ 1.71 · branching from Laplacian instability

Parameters

Particles: 1
Radius of gyration: 0
Fractal dim d_f:
Branches:
DLA (Witten-Sander 1981): Particles diffuse randomly from far away. When they touch the cluster, they stick. Tips capture more walkers (Laplacian screening) → branching fractal.

Fractal dimension: d_f ≈ 1.71 in 2D (not a simple fraction — emerges from the growth dynamics).

Laplacian growth: DLA clusters are related to viscous fingering (Hele-Shaw), dielectric breakdown, and lightning — all governed by Laplace's equation on the boundary.

Color encodes arrival time (early=blue, late=orange).