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Langton's Ant is one of a class of problem called “cellular automata" that consider the evolution of a set of coloured cells through a sequence of discrete time steps governed by rules based on the state of neighbouring cells.
An ant is placed on a universe consisting of an infinite 2D plane, divided into equally sized squares.
Only two rules apply in this imaginary universe:
- If the ant is on a white square, it must turn left and move one square forwards. The square it just left will turn black
- If the ant is on a black square, it must turn right and move one square forwards. The square it just left will turn white
When the simulation is run, the ant first passes through phases of short-term pattern-building and a breakdown into chaos.
Eventually, it begins to repeat a set of steps that build what is referred to as a “highway” leading off as far as it can be followed, emergent behaviour that can't be predicted from the rules:
