Active stresses can cause instabilities in contractile gels and living
tissues. Here we describe a generic hydrodynamic theory that treats these
systems as a mixture of two phases of varying activity and different mechanical
properties. We find that differential activity between the phases provides a
mechanism causing a demixing instability. We follow the nonlinear evolution of
the instability and characterize a phase diagram of the resulting patterns. Our
study complements other instability mechanisms in mixtures such as differential
growth, shape, motion or adhesion
