Diffusion-Limited Aggregation models Saffman-Taylor viscous fingering: a low-viscosity fluid (air) invades a high-viscosity fluid (oil) through a porous medium.
Particles perform random walks from the boundary. They stick when adjacent to the cluster with probability proportional to local curvature.
The resulting fractal has d_f ≈ 1.71 in 2D — the DLA universality class, relevant to lightning, electrodeposition, mineral dendrites.