Langton's Ant
Simple local rules produce complex emergent structure — the "highway" appears after ~10,000 steps
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About: Langton's Ant (1986) is a two-dimensional Turing machine on a grid. Rules: on a white cell, turn 90° right, flip the cell black, move forward; on a black cell, turn 90° left, flip the cell white, move forward. Despite deterministic simplicity, the ant produces chaotic patterns for ~10,000 steps, then suddenly breaks into an ordered "highway" — a repeating diagonal pattern that extends indefinitely. This is emergence: complex macro-behavior from minimal micro-rules. The highway's existence was observed empirically; a full proof remains open. Multiple ants interact and produce richer, often symmetric patterns.