PATTERN-FORMATION PROPERTIES OF AUTONOMOUS CELLULAR NEURAL NETWORKS

We use the Cellular Neural Network (CNN) to study the pattern formatio n properties of large scale spatially distributed systems. We have fou nd that the Cellular Neural Network can produce patterns similar to th ose found in Ising spin glass systems, discrete bistable systems, and the reaction-diffusion system. A thorough analysis of a 1-D CNN whose cells are coupled to immediate neighbors allows us to completely chara cterize the patterns that can exist as stable equilibria, and to measu re their complexity thanks to an entropy function. In the 2-D case, we do not restrict the symmetric coupling between cells to be with immed iate neighbors only or to have a special diffusive form, When larger n eighborhoods and generalized diffusion coupling are allowed, it is fou nd that some new and unique patterns can be formed that do not fit the standard ferro-antiferromagnetic paradigms. We have begun to develop a theoretical generalization of these paradigms which can be used to p redict the pattern formation properties of given templates. We give ma ny examples. It is our opinion that the Cellular Neural Network model provides a method to control the critical instabilities needed for pat tern formation without obfuscating parameterizations, complex nonlinea rities, or high-order cell states, and which will allow a general and convenient investigation of the essence of the pattern formation prope rties of these systems.