Diffusion-Limited Aggregation (DLA) models the Saffman–Taylor instability: particles launched from far away undergo random walks and stick upon contact with the growing cluster. The branching fractal structure (dimension ≈ 1.71 in 2D) mimics viscous fingering in Hele-Shaw cells, dendritic crystal growth, and dielectric breakdown. Higher stickiness η reduces the chance that a particle bounces and continues walking, producing denser fingers.