We consider a Cellular Neural Network (CNN) with a bias term $z$ in the integer lattice $Z^2$ on the plane $R^2$. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, $a$ and $c$, are used to describe the weights between such interacting cells. We study patterns that can exist as stable equilibria. In particular, the relationship between mosaic patterns, and the parameter space $(z, a; c)$ can be completely characterized. This, in turn, addresses the so-called "Learning Problem" in CNNs. The complexities of mosaic is also studied.