Diffusion-Limited Aggregation — Fractal Dimension

Particles released from a distant circle perform random walks until touching the growing cluster. The result: a fractal with d_f ≈ 1.71 in 2D. Screened tips grow faster, creating dendritic branching.

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Cluster size: 1 d_f ≈ -- R_max: 0

Witten & Sander (1981): DLA fractal dimension d_f ≈ 1.71 in 2D. Measured by N(R) ~ R^d_f where N(R) is number of particles within radius R. Multifractal: the growth measure (harmonic measure) has spectrum f(α). Screening: inner branches stop growing — only tips accessible to random walkers. Connection to Laplacian growth, dielectric breakdown, viscous fingering.