Particles undergo random walks until sticking to the growing cluster — fractal dimension D ≈ 1.71
1.00
10
Particles: 1
Radius: 0
Est. dim D: —
Diffusion-Limited Aggregation (Witten & Sander 1981): start with a seed particle at the center. Release particles one at a time from a random point on a large circle. Each walks randomly until it touches the cluster, then sticks with probability p (stickiness).
The resulting structure has a fractal dimension D ≈ 1.71 — it's a fractal between a line (D=1) and a filled disk (D=2). The branching pattern arises because outer tips screen interior regions from incoming particles — a mathematical analog of lightning bolts, snowflakes, mineral dendrites, and bacterial colony growth.
Lower stickiness (p < 1) gives denser, smoother aggregates by allowing particles to penetrate deeper before sticking. The fractal dimension D can be estimated from the mass-radius relation: M(r) ~ r^D.