← Algorithms

🐜 Langton's Ant

Rules: Ants: Speed:
Steps: 0
After ~10,000 steps the ant builds a "highway" repeating pattern
Langton's Ant — emergent complexity from 2 rules: on WHITE → turn right, flip black, move; on BLACK → turn left, flip white, move

🐜 Langton's Ant — Emergent Cellular Automaton

A single ant follows two rules on a grid of black and white cells: turn right on a white cell and flip it to black; turn left on a black cell and flip it to white. From this trivial ruleset, extraordinary complexity emerges.

🔬 What It Demonstrates

Langton's Ant is a two-dimensional Turing machine that demonstrates emergent complexity: after ≈10 000 steps of apparent chaos the ant spontaneously builds an infinitely repeating diagonal 'highway'. No blueprint exists — order arises purely from local rules.

🎮 How to Use

Press Play to watch the ant roam. Try Multi-Ant mode to see several ants interact, and explore Turmite rules that encode more complex behaviour. Speed slider controls the steps per frame.

💡 Did You Know?

Chris Langton introduced the ant in 1986. Despite decades of study, it is still undecidable in general whether any multi-colour ant ever builds a highway — a tiny taste of computational irreducibility.