Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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 state of each cell (or finite region) eventually periodic?

share|cite|improve this question
What kind of experimental evidence do you have for large finite approximations? – Joel David Hamkins Jun 4 '13 at 2:01

1 Answer 1

up vote 14 down vote accepted

alt text

What I get from an X of size $11121\times11121$ at just around the point where information travels to the tips.

Even from Xs ten times as long, there is Methuselah-like ebbing and flowing of debris near the center amid a pool of still lifes and blinkers still thousands of generations on.

alt text

Just going from experience working on the Busy Beaver of 5, I would imagine this question might be enormously difficult to settle, owing to the globally fractal and locally random nature of the picture.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.