Cellular Neural Networks: Space-Dependent Template, Mosaic Patterns and Spatial Chaos

We consider a Cellular Neural Network (CNN) with a bias term in the integer lattice Z on the plane Z. We impose a space-dependent coupling (template) appropriate for CNN in the hexagonal lattice on Z. Stable mosaic patterns of such CNN are completely characterized. The spatial entropy of a (p1, p2)-translation invariant set is proved to be well-defined and exists. Using such a theorem, we are also able to address the complexities of resulting mosaic patterns.