Langton’s Ant is a two-dimensional cellular automaton invented by computer scientist Chris Langton in 1986. It serves as a classic, fascinating example of emergent behavior, demonstrating how incredibly simple, deterministic rules can produce highly complex, chaotic, and eventually ordered structures. Despite having no random elements, the ant’s long-term trajectory is remarkably difficult to predict mathematically. The Two Simple Rules
The simulation takes place on an infinite grid of square cells, where every cell is initially colored white. A single virtual “ant” is placed on one cell, facing in one of the four cardinal directions.
At every discrete time step, the ant reads the color of its current square and executes three actions in sequence:
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