A defending fluid is displaced by an invader choosing the easiest neighboring throat. With a gradient (e.g. gravity or pressure), the invasion front transitions between compact and fractal morphologies.
Invaded: 0 | Front size: 0
Each site gets a random capillary threshold p ∈ [0,1]. Invader starts at top row. At each step, the boundary site with minimum p + G·y (y=depth) is invaded. G=0: fractal DLA-like cluster. G→1: compact flat front. Critical gradient separates regimes.