In this work, we explore pattern formation dynamics across a diffusively coupled Memristor Cellular Nonlinear Network (MCNN), which is composed of identical cells with locally active memristors. We bias the cells on the edge-of-chaos, introduce a systematic design procedure to induce complexity in the array, and extract the element values analytically in a parametric form. In order to enhance the stability and speed of the numerical simulations, we apply a simple variable transformation to a core memristor model while we include the additional effect of parasitic resistors to investigate the locally active dynamics of a VO₂ device. We first take a close look at the effect of the linear coupling resistor on pattern formation, and later study how nonlinearly-resistive coupling, based upon tangent hyperbolic law, affect the emergence of complex patterns. Simulation results reveal that a variety of static patterns with different characteristics can emerge across the proposed MCNN.