This paper presents results on the dynamics of asynchronous irregular cellular automata (as representations of natural information-processing systems). It is an approach to explaining global dynamics from local dynamics without the use of unrealistic intermediate structure (i.e., without synchronization or regular communication). The unrealistic intermediate structure is replaced by the the realistic assumption that local behavior is entropy reducing (an idea of E. Schrödinger).
It has been shown that, for systems composed of cells programmed as cyclic finite-state automata, the observed global oscillation can be explained in terms of the structure of attractors in the global state space. The degree of local connectivity (i.e., of communication between cells) is shown here to determine the size of global attractors, and in turn the sharpness of global behavior. However, the primary result here is the extension of these results to systems whose cells are programmed as arbitrary strongly connected automata. Finally, these phenomena are demonstrated by the simulations.