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23 votes
1 answer
2k views

Time for Langton's ant to cover a "square" torus

Langton's ant is a cellular automaton running as follows: Squares on a plane are colored variously either black or white. We arbitrarily identify one square as the "ant". The ant can travel i …
Sebastien Palcoux's user avatar
15 votes
1 answer
1k views

In how many steps a random walk visits all the elements of a finite group, with a probabilit...

This question is a variation of the return to the origin problem. Let $G$ be the finite group $\mathbb{Z}/n \times \mathbb{Z}/n$ and let the random transformation $T: G \to G$ such that $T(a,b) = ( …
Sebastien Palcoux's user avatar