WireWorld

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value  together with the number  of its eight neighbors that are set to 1 according to a system that roughly models the flow of currents in wires according to the following rules.

0. The color 0 is considered background, and always stays as background.

1. The color 1 is considered an electron head, and always turns into an electron tail.

2. The color 2 is an electron tail, and always turns into wire.

3. The color 3 is wire, which remains wire unless  is 1 or 2, in which case it becomes an electron head.

With these rules, digital logic circuits can be constructed, as illustrated above for OR, XOR, and AND gates.

In 2002, Nick Gardner demonstrated how two 8-bit binary numbers could be multiplied with a WireWorld construction using the network above.

REFERENCES:

Dewdney, A. K. "Computer Recreations.' Sci. Amer. 262, 146, Jan. 1990.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1117, 2002.