Evolving Uniform and Non-Uniform Cellular Automata Networks

Natural evolution has "created" many parallel cellular systems, in which emergent computation gives rise to impressive computational capabilities. In recent years we are witness to a rapidly growing interest in such complex adaptive systems, addressing, among others, the major problem of designing them to exhibit a specific behavior or solve a given problem. One possible approach, which we explore in this paper, is to employ artificial evolution. The systems studied are based on the cellular automata (CA) model, where a regular grid of cells is updated synchronously in discrete time steps, according to a local, identical interaction rule. We first present the application of a standard genetic algorithm to the evolution of CAs to perform two non-trivial computational tasks, density and synchronization, showing that high-performance systems can be attained. The evolutionary process as well as the resulting emergent computation are then discussed. Next we study two generalizations of the CA model, the first consisting of non-uniform CAs, where cellular rules need not be identical for all cells. Introducing the cellular programming evolutionary algorithm, we apply it to six computational tasks, demonstrating that high-performance systems can be evolved. The second generalization involves non-standard, evolving connectivity architectures, where we demonstrate that yet better systems can be attained. Evolving, cellular systems hold potential both scientifically, as vehicles for studying phenomena of interest in areas such as complex adaptive systems and artificial life, as well as practically, showing a range of potential future applications ensuing the construction of adaptive systems, and in particular `evolving ware,' evolware.