SPHERICAL CELLULAR NONLINEAR NETWORKS

We present the structures and behaviors of cellular nonlinear networks (CNN) on spheres (spherical CNN for short). Although the cells in a spherical CNN can have any number of neighbors, in this paper we study the cases where each cell has only three neighbors. We present the simulation results of symmetric and asymmetric spherical CNNs. In our simulations, we use a Bucky-ball spherical CNN structure with 60 cells and an irregular spherical CNN structure with 100 cells. Since a spherical CNN has no boundary, we use an asymmetric spherical CNN to show how information propagates on spheres via local couplings. We also show that if a spherical CNN is locally active then different patterns can be found in its stable output.