[[wp:Langton's ant|Langton's ant]] is a cellular automaton that models an [https://en.wikipedia.org/wiki/Ant ant] sitting on a plane of cells, all of which are white initially, the ant facing in one of four directions.
<br>This rather simple ruleset leads to an initially chaotic movement pattern, and after about 10000 steps, a cycle appears where the ant moves steadily away from the starting location in a diagonal corridor about 10 cells wide.
Conceptually the ant can then walk infinitely far away.
Start the ant near the center of a 100<small>x</small>100 field of cells, which is about big enough to contain the initial chaotic part of the movement.