Grid cells, which were first discovered in the entorhinal cortex of mammals, are normatively thought of as instrumental in spatial navigation because of their periodic firing characteristics as the animal traverses its surroundings. In recent years, converging bodies of evidence from etiological and teleological investigations of grid cells indicate that they arise under efficient coding schemes, with metabolic, sparsity, and nonnegativity constraints supporting the formation of regular lattices that approximate what has been observed in animal experiments. Here we import the notion of local activity, a circuit-theoretic concept proposed by Leon Chua to formalize Prigogine's idea of "instability of the homogeneous," as a new approach towards understanding the emergence of grid-like representations in the brain. Using the Schnakenberg model as a reaction-diffusion system endowed with Turing instability, we identified regions in the parameter space corresponding to the locally active regime—i.e, the stability boundary between the stable and unstable domains, S(Q1)A(Q1) and A(Q1)U(Q1)), respectively—that appear to promote the formation of grid patterns resembling firing fields of grid cells. Furthermore, we explore how a subset of the locally active regime within the state space, dubbed the "edge of chaos," may delineate the conditions for the formation of regularly-spaced grid patterns by naturally identifying the optimal range of model parameters in cellular nonlinear networks that drive internal grid attractor dynamics. Through this research, we aim to better understand the constraints that result in the canonical representation of space and ordered experience which, in turn, informs decisions and organizes behavior.