Langton’s Ant

Chaos, then a highway

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Langton’s ant: turn right on white, left on black, flipping the colour.
• After about 10,000 chaotic steps, it builds an endless highway.
• Nobody has proved it always does: simple rules, hard proofs.

Steps

1. An ant with two rules
2. The first few steps
3. Watch it wander
4. Always a highway?
5. The fifth step
6. Highway speed