Simple Rules, Emergent Complexity, and the Highway to Infinity
Classic RL
Multi-Rule
Multi-Ant
Heat Map
About Langton's Ant
Discovered by Christopher Langton in 1986, this simple cellular automaton demonstrates how complexity emerges from simple rules:
Rule: At a white cell, turn 90° right (R), flip color, move forward. At a black cell, turn 90° left (L), flip color, move forward.
Initial Chaos: The ant creates seemingly random patterns for the first ~10,000 steps
Highway Emergence: After chaos, the ant builds a repeating "highway" that extends forever
Turing Complete: Can be used to perform universal computation
No Proven Limit: It's unproven whether the ant always builds a highway from any starting condition
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Steps
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Cells Flipped
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Grid Size
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Cells Visited
Multi-Color Rules
Extend Langton's Ant to multiple colors and rules. Each letter in the rule string represents a turn direction:
L = Turn 90° left
R = Turn 90° right
Rule Length: Determines number of colors (RLR = 3 colors, LLRR = 4 colors)
Famous Rules: RLR creates symmetric patterns, LLRR makes triangular structures, RLLR builds highways
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Steps
RLR
Current Rule
3
Colors
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Cells Visited
Multiple Ants Simultaneously
Watch multiple ants with different rules and colors interact on the same grid. Each ant follows its own rule, but they all affect the same cells, creating emergent interference patterns.
Ant Configuration
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Steps
2
Active Ants
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Collisions
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Cells Visited
Cell Visit Frequency Heat Map
Visualize how many times each cell has been visited. Colors represent visit frequency: