two rules. a grid. chaos for 10,000 steps. then, inexplicably, a highway.
The ant follows just two rules on each step:
· if the cell is white → turn right 90°, flip the cell to black, move forward.
· if the cell is black → turn left 90°, flip the cell to white, move forward.
For the first ~10,000 steps, the trail looks random. Then — suddenly — the ant starts building a repeating diagonal highway, 104 steps per cycle, forever. Nobody proved this would happen. It just does.
step
0
black cells
0
speed
1×
phase
chaos
speed
highway: not yet
what to watch for
~350first chaotic bursts, loose symmetry
~2,500visible structure, but still messy
~10,000highway begins. the ant escapes in a diagonal line, forever.
104steps per highway cycle. 2 cells diagonal per cycle.