Pattern formation in a monolayer of magnetic spheres.

Pattern formation is investigated for a vertically vibrated monolayer of magnetic spheres. The spheres of diameter D encase cylindrical magnetic cores of length l. For large D/l, we find that the particles form a hexagonal-close-packed pattern in which the particles' dipole vectors assume a macroscopic circulating vortical pattern. For smaller D/l, the particles form concentric rings. The static configurational magnetic energy (which depends on D/l) appears to be a determining factor in pattern selection even though the experimental system is driven and dissipative.