Langton's ant · order from chaos simulation

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?

▶ Run the simulationSee the measured result

Units: steps per highway cycle (exact integer; secondary knowns: drift (−2,−2), escape speed √8/104 = 0.027196414, onset ≈ 10⁴, diffusive exponent ½ for the memoryless rival)

How the lab tests it

Two 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.

What it checks

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