Ferrofluid Interface: Fourier-Mode Dispersion

This is the 2D counterpart to the 3D Hele-Shaw ferrofluid grid simulation. Instead of a cellular-automaton lattice, it represents the fluid/air boundary as a sum of angular Fourier modes and integrates each mode's amplitude directly from a magnetic-vs-tension dispersion relation, with a cubic saturation term that selects a stable finger spacing once growth saturates. The result is the same physical competition — magnetic surface energy elongating the interface, surface tension shortening it — computed as an explicit ODE system rather than approximated by local growth probabilities, so you can watch the dominant wavenumber shift live as you move the field and tension sliders.