Langton’s Ant is a cellular automaton representing an ant's movement on a grid of cells based on simple rules.
At the onset of the simulation, the ant is placed randomly on a 2D-grid consisting of white cells and given a direction (up, down, left, or right).
The movement of the ant is determined by the color of the cell it occupies, following these rules:
- If the cell is white, it transitions to black, and the ant turns clockwise 90°.
- If the cell is black, it changes to white, and the ant turns counterclockwise 90°.
- The ant then advances to the adjacent cell and repeats from step 1.
These elementary rules give rise to intricate behaviors. When starting on a fully white grid, three discernible modes of behavior emerge:
- Simplicity: In the initial moves, simple symmetric patterns are formed.
- Chaos: After several hundred moves, a large irregular pattern of black and white squares emerges. The ant navigates a pseudo-random path until approximately 10,000 steps.
- Emergent order: Eventually, the ant begins constructing a repeating "highway" pattern consisting of 104 steps that continues indefinitely.
All tested finite initial configurations eventually reach the same repetitive pattern. This suggests that the "highway" serves as an attractor for Langton's Ant. Nevertheless, there is no conclusive proof that this holds true for all such initial setups.
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