Active stresses can cause instabilities in contractile gels and living tissues. Here we provide 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 causes a uniform mixture to
undergo 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 driven
by differential adhesion, differential diffusion, differential growth, and differential motion.