We propose a method for mapping a spatially discrete problem. stemming from the spatial discretization of a parabolic or hyperbolic partial differential equation of gradient type, to a heterogeneous one with certain comparable dynamical features pertaining. in particular, to coherent structures. We focus the analysis on a (1 + 1)-dimensional phi (4) model and confirm the theoretical predictions numerically. We also discuss possible generalizations of the method and the ensuing qualitative analogies between heterogeneous and discrete systems and their dynamics.