Labyrinthine pattern formation in magnetic fluids.

A quasi two-dimensional drop of a magnetic fluid (ferrofluid) in a magnetic field is one example of the many systems, including amphiphilic monolayers, thin magnetic films, and type I superconductors, that form labyrinthine patterns. The formation of the ferrofluid labyrinth was examined both experimentally and theoretically. Labyrinth formation was found to be sensitively dependent on initial conditions, indicative of a space of configurations having a vast number of local energy minima. Certain geometric characteristics of the labyrinths suggest that these multiple minima have nearly equivalent energies. Kinetic effects on pattern selection were found in studies of fingering in the presence of timedependent magnetic fields. The dynamics of this pattern formation was studied within a simple model that yields shape evolutions in qualitative agreement with experiment.