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31 votes
1 answer
1k views

Vanishing line on Conway's game of life

If the initial state of Conway's game of life is a line of $n \in [0,100]$ alive cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$. ...
Sebastien Palcoux's user avatar
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 in ...
Sebastien Palcoux's user avatar
13 votes
1 answer
597 views

Does Langton's ant cover every n by 6 gridded torus?

This post follows this other post about times cover by Langton's ant of $n$ by $n$ gridded torus. For $n$ by $n$ gridded torus, I've checked for $n \le 1000$ that the ant covers all. This fact needs ...
Sebastien Palcoux's user avatar
8 votes
1 answer
436 views

The graph of Rule 110 and vertices degree

Consider the elementary cellular automaton called Rule 110 (famous for being Turing complete): It induces a map $R: \mathbb{N} \to \mathbb{N}$ such that the binary representation of $R(n)$ is ...
Sebastien Palcoux's user avatar