🐜 Langton's Ant
Langton's Ant is a two-dimensional Turing machine with surprisingly complex emergent behaviour from just two rules: when on a white cell, turn right 90°, flip the cell to black, move forward; when on a black cell, turn left 90°, flip the cell to white, move forward (RL rule). After an initial chaotic phase (~10,000 steps), the ant spontaneously builds a periodic diagonal highway that repeats every 104 steps — a classic example of emergence. Generalised turmites use more colours; select a preset rule to explore them. 🇺🇦 Українська
Ant rule
Emergence and Turing completeness
Despite the trivial rule set, Langton's Ant is Turing-complete: any computation can be encoded in its grid state. The emergent highway was proved never to be stationary (Chris Langton, 1986); whether the ant always eventually builds a highway for any finite initial configuration remains an open conjecture. Multi-colour generalisations (turmites) can generate space-filling curves, symmetric patterns, and fractal-like structures — explored through the preset rules above.