MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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
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.