# Wireworld

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

Wireworld is a 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.

## Rules

Example of a complicated circuit made in WireWorld: a seven segment display and decoder. Conductor cells are dark green to highlight signal flow and display segments.

A Wireworld cell can be in one of four different states, usually numbered 0–3 in software, modeled by colors in the examples here:

1. Empty (Black)
3. Electron tail (Red)
4. Conductor (Yellow)

As in all cellular automata, time proceeds in discrete steps called generations (sometimes "gens" or "ticks"). 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, or remains Conductor otherwise.

Wireworld uses 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, both orthogonal and diagonal.

These simple rules can be used to construct logic gates (see below).

2 Clock generators sending electrons into an XOR gate

## Applications

Entities built within Wireworld universes include Langton's Ant (allowing any Langton's Ant pattern to be built within Wireworld),[2] and the Wireworld computer, a turing-complete computer implemented as a cellular automaton.[3]

## Computer programs featuring Wireworld

The Powder Toy Wireworld WIRE Displaying The Number 9
• Wireworlds: the classical Wireworld cellular automaton and many variations. Game contains about 100 examples of logical gates etc. created in Wireworld.
• 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.
• Golly: Probably the fastest way to run large Wireworld configurations. The Wireworld computer is supplied in the examples.
• Wireworld player: A Flash-based Wireworld simulator, with support for plain-text and MCell formats.
• Xlife: Probably the fastest way to run Wireworld patterns in the step-by-step mode.
• Wiresq: a music synthesizer for iOS devices.
• The Powder Toy: a computer based sandbox particle simulation program, featured in v55.1+.