Classical cellular automata

In the previous chapter we gave some examples of discrete time (DT) processes involving a small number of dynamical variables. However, the world around us is a complicated dynamical system with a truly vast number of degrees of freedom. Therefore, we should be prepared to discuss DT models with arbitrary numbers of degrees of freedom. In particular, we should be interested in cellular automata (CAs), models representing dynamical variables filling all of physical space.

Physical space is the three-dimensional arena of position that we see all around us and in which particle systems under observation (SUOs) appear to move. We shall not debate the question of whether physical space is real, a relational manifestation or a mental construct. For all practical purposes, CA theory requires us to think of it as real, particularly in computer simulations, where specific cells in the CA are given individual array labels that persist throughout a simulation. We shall see this explicitly when we come to discuss spreadsheet mechanics later on in this chapter.

In the applications that we investigate in this chapter, the architecture is that of DT evolution in a fixed background universe, shown in Figure 5.1(b). In Chapter 29 we discuss the scenario of a CA with an evolving background universe as shown in Figure 5.2.

It is important to distinguish physical space from configuration space, the mathematical space representing all the spatial dynamical degrees of freedom used to describe a many-particle SUO.