Langton's ant

Langton's ant is a two-dimensional Turing machine with a very simple set of rules, invented by attractor of Langton's ant.

Langton's ant can also be described as a cellular automaton, where most of the grid is colored black or white, and the "ant" square has one of eight different colors assigned to encode the combination of black/white state and the current direction of motion of the ant.

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Extension to Langton's ant

There is a simple extension to Langton's ant where instead of just two colors, more colors are used. The colors are modified in a cyclic fashion. There is also a simple name giving scheme for such ants: for each of the successive colours, a letter 'L' or 'R' is used to indicate whether a left or right turn should be taken. Langton's ant would get the name 'RL' in this name giving scheme.

Some of these extended Langton's ants produce patterns that become symmetric over and over again. One of the simplest examples is the ant 'RLLR'. One sufficient condition for this to happen is that the ant's name, seen as a cyclic list, consists of consecutive pairs of identical letters 'LL' or 'RR' (the words "seen as a cyclic list" imply that the last letter may pair with the first one.)


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