9
votes
1answer
381 views

The infinite X in Conway's game of life

In Conway's game of life, take the initial position to be two infinite diagonal lines of live cells, with a single cell in common. Does this thing converge to a stable configuration? I.e., is the ...
23
votes
2answers
650 views

Is there any superstable configuration in the game of life?

This question spins off of Gil Kalai's recent question on Conway's game of life for a random initial configuration. There are numerous configurations in the game of life that are known to be ...
37
votes
7answers
3k views

Conway's game of life for random initial position

What is the behavior of Conway's game of life when the initial position is random? -- We can ask this question on an infinite grid or on an $n$ by $n$ table (planar or on a torus). Specifically ...