What is a Cellular Automaton?

Part of:
"The Universe in Black and White," by Graham Farmelo, The Daily Telegraph, January 13, 1999.

In a chess-board cellular automaton, a simple set of rules determines how the pattern of squares on one horizontal row is related to the pattern on the row below. An example is the very simple cellular automaton below. The simple set of rules below ensure that the pattern builds a single black square (step 1) to an expanding pyramid shape. The set of rules comprise eight separate rules, each of which dictates how a sequence of three squares in a row determines whether the square in the next row below the middle square is black or white.

For example, in the rule to the left, three black squares in a row means that the middle square has a black square underneath. In the same rule, two black squares followed by a white square also leads to a black square below the middle one. Every chessboard cellular automaton is determined by a set of eight rules like this, implying that there is a total of 256 automata. Stephen Wolfram was the first to observe the various patterns produced by these types of cellular automata.

The Rule 30 Automaton

This cellular automaton, based on the rule shown above, has a remarkably complex pattern even though is evolves from the simplest possible beginning, a single black square. While he was pondering this pattern, it gradually dawned on Wolfram that simple programs (sets of rules) could provide the key to an understanding of the complexities of nature. He now believes that the language of the science of the future will be patterns, not equations.