A less-viscous fluid invades a more-viscous one in a Hele-Shaw cell, forming fractal fingers via interfacial instability.
Saffman & Taylor (1958): when a less-viscous fluid (air) displaces a more-viscous fluid (oil) in a thin gap, the flat interface is unstable. Linear growth rate σ(k) = (M−1)/(M+1)·|k|·U − B·k³/(M+1). Fingers form, compete, and the widest finger typically wins (tip-splitting only with surface tension). This simulation uses a diffusion-limited aggregation analogy with pressure-driven random walk.