← back Paterson's Worms

Origin

Mike Paterson and John Conway, 1971. First described by Martin Gardner in Scientific American, 1973. MathWorld. One variant's fate is still mathematically unknown.

How It Works

A worm moves on a triangular lattice with 6 directions per node. At each intersection, it checks which paths have been eaten. Based on a fixed rule table, it chooses the next uneaten direction. Different rule tables produce spirals, space-fillers, or worms that halt after millions of steps.

Applications

Open mathematical problems in computability. Produces hexagonal snowflake-like trail patterns unique to the triangular grid.

choose a preset worm species·speed controls steps per frame·random generates unexplored worm types
running