Ferrofluid Labyrinthine Instability

Inside a Hele-Shaw cell — two glass plates a hair's-width apart — a ferrofluid droplet held under a perpendicular magnetic field does not stay round. Magnetic surface energy pushes the fluid/air interface to elongate while surface tension resists, and the resulting tug-of-war produces the same kind of pattern-forming instability seen in viscous fingering and dendritic growth: a self-organizing maze of branching fingers whose spacing is set by a real dispersion relation between the two competing terms. This simulation renders that growth front on a live 3D grid, with independent control over field strength and surface tension so you can watch fine branching fingers give way to smooth, coarse lobes and back again.