Wireworld

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2 Wireworld diodes, the above one in conduction direction, the lower one in reverse-biasing

Wireworld is a well-known cellular automaton first proposed by Brian Silverman in 1987, as part of his program Phantom Fish Tank. It subsequently became more widely known as a result of an article in the "Computer Recreations" column of Scientific American.^[1] Wireworld is particularly suited to simulating electronic logic elements, or "gates", and, despite the simplicity of the rules, Wireworld is Turing-complete^{[citation needed]}.

1 Rules
2 Applications
3 Computer programs featuring Wireworld
4 See also
5 References

Rules

A Wireworld cell can be in one of four different states:

Empty
Electron head
Electron tail
Conductor

Note that in software these states are often numbered 0-3 rather than 1-4. In the examples on this page, the states are displayed as colours proceeding: black, blue, red, yellow. These colours are in no way standardized.

Like in all cellular automata time proceeds in discrete steps called generations (sometimes "gens" for short). Cells behave as follows:

Empty → Empty
Electron head → Electron tail
Electron tail → Conductor
Conductor → Electron head if exactly one or two of the neighbouring cells are electron heads and remains Conductor otherwise.

Wireworld has what is called the Moore neighborhood, which means that in the rules above, neighbouring means one cell away (range value of one) in any direction (orthogonal and diagonal).

Using just these simple rules we can begin to construct gates (see below).

2 Clock generators and an XOR gate

Applications

Notable entities built within Wireworld universes include a computer which tests odd positive integers (and 2) for primeness^[2], and unit cells for another cellular automaton; Langton's Ant (allowing any Langton's Ant pattern to be built within Wireworld).^[3]

Computer programs featuring Wireworld

Wireworlds: the classical Wireworld cellular automaton and many variations. Game contains about 100 examples of logical gates etc created in Wireworld.
JavaScript Simulator: a Wireworld simulation program
A Wireworld Computer: an account of the construction of a full-scale computer using wireworld.
MCell: A free program for running cellular automata, can run Wireworlds.
[1]: Article about wireworld automata.

References

^ Computer recreations: The cellular automata programs that create Wireworld, Rugworld and other diversions, Scientific American (1990) by A K Dewdney
^ Mark Owen. "The Wireworld Computer".
^ Nyles Heise. "Wireworld".