Langton’s Ant

Langton’s Ant lives on a grid of colored squares. At each step, the ant turns left or right depending on the color of its current square. Additionally, the ant changes the color of the square it just left. The system displays interesting behavior with even the simplest rules (2 possible colors) With this minimal rule set, the ant moves with no discernible pattern for around 10,000 steps, then falls into an infinitely repeating pattern of 104 steps (see the video). More complicated rules result in other interesting steady state behaviors. The way that Langton’s ant modifies its own world, thereby affecting its own future behavior, is reminiscent of nonlinear systems, where “playing the game has a way of changing the rules.”

For more information, see http://mathworld.wolfram.com/LangtonsAnt.html

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