We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z2 on the plane R2. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and ε, 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; ε) can be completely characterized. This, in turn, addresses the so-called learning problem in CNNs. The complexities of mosaic patterns are also addressed.