Langton's ant

Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complex emergent behavior.

It is only known that the ant's trajectory is always unbounded regardless of the initial configuration[4] – this result was incorrectly attributed and is known as the Cohen-Kong theorem.

[5] In 2000, Gajardo et al. showed a construction that calculates any boolean circuit using the trajectory of a single instance of Langton's ant.

One sufficient condition for this to happen is that the ant's name, seen as a cyclic list, consists of consecutive pairs of identical letters "LL" or "RR".

[7] Multiple Langton's ants can co-exist on the 2D plane, and their interactions give rise to complex, higher-order automata that collectively build a wide variety of organized structures.