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2 questions
23
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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 in
...
15
votes
1
answer
1k
views
In how many steps a random walk visits all the elements of a finite group, with a probability 1/2?
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) = (...