Can a rule small enough to fit on a napkin — a single 'ant' that turns by the colour of the square it stands on — produce order, and how do you know it's not just noise?
▶ Launch the interactive simulationTwo lines: on a WHITE cell turn right, flip it black, step; on BLACK turn left, flip it white, step. Run it on a blank boundary-free grid and read the trajectory: detect the period of any eventual cycle, its per-cycle drift, and the step at which order locks in — no tuning, no seed.
three regimes from one rule: ~500 steps of SIMPLE symmetric doodles, then ~10,000 steps of apparent CHAOS (a pseudo-random blob hugging the origin), then — unforced — an emergent HIGHWAY: an exactly periodic cycle of period 104 that lays a repeating diagonal road and carries the ant to infinity at √8/104 ≈ 0.0272 cell·step⁻¹. Measured period and drift are exact integers; the onset step is empirical (~10⁴). Two hard results frame it: Cohen–Kong (1988) PROVED the trajectory is always unbounded for any finite start, and with richer initial tapes the ant is Turing-complete (Gajardo–Moreira–Goles 2002) — order, and universal computation, out of two lines