This paper presents the analytical investigation of complex pattern formation in a Memristor Cellular Nonlinear Network (M-CNN) by applying the theory of local activity. The proposed M-CNN has the conventional two dimensional (2D) planar structure, where all the memristive cells are identical and resistively coupled to each other. The single cell is composed of a suitable combination of a DC voltage source, a bias resistor, a locally active NbOx memristor, and a capacitor. The locally active memristor has a simplified generic form, enhancing the simulation speed, and a functional AC equivalent circuit, facilitating further inspections. The stability analysis of the single cell is followed by the extraction of the parameters of the local activity, edge-of-chaos, and sharp-edge-of-chaos domains. Simulation results demonstrate that pattern formation can emerge in a dissipatively coupled M-CNN with locally active memristors.