One ant, two rules: on white turn right, on black turn left, flip the square, step forward. For about ten thousand steps it makes senseless mess — then, from nothing in the rules that predicts it, it builds a highway and drives off forever. Slide the clock and watch order arrive on schedule.
The grid starts all white. Each step: read the ant’s cell; turn right if white / left if black; flip the cell; advance. That is the whole program. Emergence is the surprise: after ~10,000 steps the trajectory locks into a period-104 cycle that translates diagonally — the ‘highway’. A fail-loud self-check runs 11,000 steps and throws unless the displacement over one 104-step window equals the next (a genuine repeating highway), a fact provable for no ant from its two rules alone.
That the highway ALWAYS emerges from a single ant on a blank grid is an empirical theorem (open in general for arbitrary finite start states); here it is exhibited, and the period-104 repeat is checked exactly.