ABSTRACT
Imagine you have a piece of square graph paper and a marker pen. You colour in some of the squares in the first column of the paper, leaving others blank. You then move to the second column, and colour in squares in this according to some rule relating to the position of coloured squares in the first column. For example, the rule could be that for every coloured square in column 1, the equivalent square in column 2 is left blank, and every blank in column 1 becomes coloured in column 2. Imagine you now repeat this process for several thousand iterations to see what pattern of coloured squares arises. This setup captures in essence what is known as a cellular automaton in computer science. A cellular automaton is a grid with initial conditions and a set of rules for propagating those initial conditions across the grid. Cellular automata are the basis behind Conway’s famous Game of Life (Conway 1970). For the vast majority of initial conditions and rules the Game of Life is uninteresting, either completely random or highly predictable distributions are produced. But for some combinations of rules and initial conditions, striking, almost life-like, distributions arise. These distributions are complex, existing in the hinterland between randomness and regularity. Even though all the rules of the Game of Life, and all the initial conditions, are known perfectly, structures can still appear which defy prediction from that perfect knowledge of the system.
