Reaction–diffusion equations are ubiquitous in population dynamics, laser physics, bacterial growth, domain wall kinetics, order parameter relaxation and a host of other problems, cutting across disciplines. The occurrence of nonlinearity adds further complexity in terms of bifurcation-solutions, phase transitions, fractalgrowth, etc. In most cases the non-transient, asymptotic solutions of these equations lead to patterns, the nature of which depends on certain symmetry properties of the underlying variable(s). In this paper we discuss a few suchequations with applications to domain motion of different kinds in ferroelectrics, multiferroics and their switching characteristics because of the underlying nonlinearities, and glucose-induced fractal colony growth of Bacillus thuringiensis.