A Simple Cellular Automaton That Solves the Density and Ordering Problems

Cellular automata (CA) are discrete, dynamical systems that perform computations in a distributed fashion on a spatially extended grid. The dynamical behavior of a CA may give rise to emergent computation, referring to the appearance of global information processing capabilities that are not explicitly represented in the system’s elementary components nor in their local interconnections. As such, CAs offer an austere yet versatile model for studying natural phenomena, as well as a powerful paradigm for attaining fine-grained, massively parallel computation. An example of such emergent computation is to use a CA to determine the global density of bits in an initial state configuration. This problem, known as density classification, has been studied quite intensively over the past few years. In this short communication we describe two previous versions of the problem along