How can it evolve?
I'm confused by the sentence "Much later it will be dominated by simple infinite growth patterns." Does "much later" mean "after many generations"? Isn't it (after less than about 10 generations) a stable constellation of blocks and blinkers? How can that ever change by itself? Micromegas (talk) 09:41, 28 February 2018 (UTC)
- Yes, "much later" means "after many generations". My reading of that section is this: if you seed the entire (!) universe with s small but non-zero initial density ε, then a) after "a few" generations, most (not all!) objects that haven't died from underpopulation will be blocks and blinkers; and b) any pattern will appear somewhere in the universe with a non-zero probability. Those patterns include infinite-growth patterns; it will take a while for them to "get started", but by definition they'll grow indefinitely, and eventually they'll "take over" as the dominant feature in the universe, in the sense that the probability of any object/live cell/active section of the universe belonging to (having been produced by) an infinite growth pattern will approach 1.
- That matches my understanding. The eventual fate of infinite Life universes is very painfully hard to think about. If there is a spacefiller or quadratic-growth replicator pattern that can spread through a sparse scattering of blocks and blinkers, then it's bound to show up somewhere in the infinite universe. In fact, an unlimited number of copies will show up somewhere -- the question is just what they'll run into and get destroyed by, before they get to the point in the universe that you're looking at.
- At the moment I _think_ (but don't quote me on it) that the super-rare quadratic-growth stuff will be the most likely to run into some kind of switch-engine debris, with very-near-zero odds of hitting other stuff like glider streams from guns, or pufferfish exhaust. But it's conceivable that something could be discovered that would change the details of the calculation. See, e.g., Nick Gotts' article "Emergent Complexity in Conway’s Game of Life", summarized here. Dvgrn (talk) 17:12, 28 February 2018 (UTC)