Chalkdust, Issue 13

chalkdust

On the cover

Cellular automata Matthew Scroggs

T

he game of life—invented by John Conway (see pages 56–57) in 1970—is perhaps the most famous cellular automaton. Cellular automata consist of a regular grid of cells (usually squares) that are (usually, see page 38) either ‘on’ or ‘off’. From a given arrangement of cells, the state of each cell in the next generation can be decided by following a set of simple rules.

Surprisingly complex patterns can often arise from these simple rules.

While the game of life uses a two-dimensional grid of squares for each generation, the cellular automaton on the cover of this issue of Chalkdust is an elementary cellular automaton: it uses a one-dimensional row of squares for each generation. As each generation is a row, subsequent generations can be shown below previous ones.

Elementary cellular automata In an elementary cellular automaton, the state of each cell is decided by its state and the state of its two neighbours in the previous generation.

An example such rule is shown to the right: in this rule, the a cell will be on in the next generation if it and its two neighbours are on–off–on in the current generation. A cellular automaton is defined by eight of these rules, as there are eight possible states of three cells.

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1 An example rule spring 2021