What is Wireworld?

What is Wireworld?

Wireworld is a cellular automaton on an infinite square grid, invented by Brian Silverman in about 1984. It appeared as part of his ‘Phantom Fish Tank’ program in 1987, but we only found out about it when it was described in Scientific American in January 1990. The automaton has a similar flavour to J. H. Conway’s well-known ‘Game of Life’.

The elements of Wireworld

Each cell can be in one of four different states, forming a pattern on the grid. The four states are:

• blank, shown in the pictures here in black;
• ‘copper’, shown here as a sort of orange colour;
• ‘electron head’, or just ‘head’ for short, shown here as white; and
• ‘electron tail’, or ‘tail’, shown in blue.

Blank	Copper	Head	Tail

The rules of Wireworld

Time proceeds in discrete steps called generations. At each generation the state of each cell may change; whether it changes, and what it changes to, depend on its current state and the state of its eight nearest neighbour cells according to a simple set of rules:

• a blank square always stays blank
• an electron head always becomes an electron tail
• an electron tail always becomes copper
• copper stays as copper unless it has just one or two neighbours that are electron heads, in which case it becomes an electron head

We can set up any desired initial state on the grid and observe its evolution over a number of generations. The pattern below consists of a single row of copper cells with an electron head-tail pair on it. What happens when we let it evolve?

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