Talk:Infinite growth
Revision as of 14:18, 22 August 2012 by Spam User (talk | contribs) (moved Talk:Infinite growth to Talk:Chicken Noodle Soup)
Fastest?
"quadratic growth is the fastest possible growth rate"
I don't believe this is correct. Is there some reason you can't have a factory that produces MMM breeders? --Axaj 02:33, 20 October 2009 (UTC)
- Quadratic is the fastest possible because patterns can't possibly expand at a speed faster than c. Thus, if the bounding box is x-by-y to begin with, after k generations it is at most (x+2k)-by-(y+2k), which has area xy+2k(x+y)+4k^2, which is quadratic in k. Since the area of the bounding box is an upper bound on the number of alive cells in the pattern, the number of alive cells can't grow any faster than quadratically. Nathaniel 03:28, 20 October 2009 (UTC)
- Okay, I see now. Thanks! --Axaj 15:03, 25 October 2009 (UTC)