Quasi-uniform computation-universal cellular automata

Abstract

Cellular automata (CA) are dynamical systems in which space and time are discrete, where each cell obeys the same rule and has a finite number of states. In this paper we study non-uniform CA, i.e. With non-uniform local interaction rules. Our focal point is the issue of universal computation, which has been proven for uniform automata using complicated designs embedded in cellular space. The computation-universal system presented here is simpler than previous ones, and is embedded in the minimal possible two-dimensional cellular space, namely 2-state, 5-neighbor (which is insufficient for universal computation in the uniform model). The space studied is quasi-uniform, meaning that a small number of rules is used (our final design consists of just two rules which is minimal), distributed such that most of the grid contains one rule except for an infinitely small region which contains the others. We maintain that such automata provide us with a simple, genera/model for studying Artificial Life phenomena.