Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid-air interface

Spontaneous pattern formation by self-assembly is of long-standing(1-3) and continuing interest(4,5) not only for its aesthetic appeal(6,7), but also for its fundamental(8-18) and technological relevance(19). So far, the stud y of self-organization processes has mainly focused on static structures, b ut dynamic systems(20-22) - those that develop order only when dissipating energy - are of particular interest for studying complex behaviour(23,24). Here we describe the formation of dynamic patterns of millimetre-sized magn etic disks at a liquid-air interface, subject to a magnetic field produced by a rotating permanent magnet. The disks spin around their axes with angul ar frequency equal to that of the magnet, and are attracted towards its axi s of rotation while repelling each other. This repulsive hydrodynamic inter action is due to fluid motion associated with spinning; the interplay betwe en attractive and repulsive interactions leads to the formation of patterns exhibiting various types of ordering, some of which are entirely new. This versatile system should lead to a better understanding of dynamic self-ass embly, while providing a test-bed for stability theories of interacting poi nt vortices(25-28) and vortex patches(29).