  Active forces occurring within cells can drive crucial biological processes
that involve spontaneous organization and shape change, such as cell division.
Motivated by recent in vitro experiments of nematic droplets of cytoskeletal
filaments and motors that self-organize and divide, we present a minimal
hydrodynamic model that combines the nonequilibrium kinetics of motor-filament
interactions with equilibrium nematic phase separation. The motors organize
within droplets and structure filaments into polarized aster defects. At large
motor activity, they can even deform or divide the droplet, or form multi-aster
chains of droplets. Our predicted phase diagram recapitulates these
experimentally observed shapes.
