  We study numerically the behaviour of a mixture of a passive isotropic fluid
and an active polar gel, in the presence of a surfactant favouring
emulsification. Focussing on parameters for which the underlying free energy
favours the lamellar phase in the passive limit, we show that the interplay
between nonequilibrium and thermodynamic forces creates a range of multifarious
exotic emulsions. When the active component is contractile (e.g., an actomyosin
solution), moderate activity enhances the efficiency of lamellar ordering,
whereas strong activity favours the creation of passive droplets within an
active matrix. For extensile activity (occurring, e.g., in microtubule-motor
suspensions), instead, we observe an emulsion of spontaneously rotating
droplets of different size. By tuning the overall composition, we can create
high internal phase emulsions, which undergo sudden phase inversion when
activity is switched off. Therefore, we find that activity provides a single
control parameter to design composite materials with a strikingly rich range of
morphologies.
