Symmetry properties of cellular neural networks on square and hexagonal grids

It is pointed out that while the symmetry inherent in a given problem should be reflected in the structure of a CNN designed to solve it, the degree of symmetry possible in the network is limited to the symmetry group of the grid it is defined on. The exact numbers of independently choosable entries in both square and hexagonal CNN-templates with different important kinds of symmetry are compared. As expected, the higher symmetry of the hexagonal grid leads to a significant reduction in the complexity of the templates