Mathematics · Study 048
Langton's Ant
An ant turns right on white, left on black, and flips the square it leaves. After about 10,000 chaotic steps it starts building a highway.
What you're looking at
The ant stands on a grid of white cells. On a white cell it turns right, on a black cell it turns left. Either way it flips the colour of the cell and steps forward. For the first several hundred steps the trail looks symmetric, then it dissolves into a messy blob.
The idea behind it
Around step 10,000 something changes. The ant falls into a cycle of 104 steps that shifts it diagonally, and it marches off building a repeating strip forever. Chris Langton described the system in 1986. Every starting pattern ever tested ends in a highway, and nobody has proved that all of them must.
Try this
Click or tap to drop another ant. Two ants can build, collide and even undo each other's work.
