Particles perform random walks until they stick to the growing cluster. The resulting fractal has Hausdorff dimension ≈ 1.71 in 2D.
Particles: 0 | Radius: 0
DLA (Witten-Sander 1981): A paradigmatic model of fractal growth. The fractal dimension d_f ≈ 1.71 arises from the screening effect — fjords become inaccessible to diffusing particles, amplifying tip growth.
DLA describes: electrodeposition, dielectric breakdown, viscous fingering (Hele-Shaw cell), mineral dendrites, coral growth, lightning channels. Key insight: The cluster solves the Laplace equation ∇²φ=0 outside — growth probability ∝ |∇φ|. This makes DLA equivalent to the classical problem of diffusion to an absorbing boundary.