Talk:Garden of Eden pattern

From Wikipedia, the free encyclopedia

You have new messages (last change).

Eric119 added "Actually, all non-bijective automata possess Garden of Eden patterns." This is clearly true if it were "non-surjective", but consider a CA which is surjective but not injective. Thus it is not bijective, but would not have GoE states as the CA is surjective.

Is non-bijective what was meant, and that I'm wrong somehow, or was non-surjective the desired description? Dysprosia 23:24, 5 Jun 2005 (UTC)

All non-injective automata must be non-surjective, according to Cellular automaton#Reversible cellular automata. Eric119 23:55, 5 Jun 2005 (UTC)
How does that section say that? I think I see that consequence now, regardless... Dysprosia 00:51, 6 Jun 2005 (UTC)

I think the "non-injective leads to garden of eden" deserves a reference. Looking at weissteins page, it's probably that theorem by Edward Moore, but I havn't been able to track down the paper

I don't understand this sentence: "Garden of Eden patterns are necessarily unique." Unique per automaton? That can't be the case, since the page lists more than one GOE pattern for the Game of Life. So in what sense are they unique? --Eriatarka 11:45, 17 March 2007 (UTC)

Until recently that sentence said, "not necessarily unique". Someone removed the word "not", which I have restored. Eric119 17:31, 17 March 2007 (UTC)
Okay... but now the fact that they're not necessarily unique seems about as noteworthy as the fact that they're not necessarily square, or not necessarily symmetrical. Some version of this sentence has been in there from the beginning (and a previous attempt to remove it was reverted, I see.) The sentence started out as "Garden of Life [sic] patterns are not unique." However, the original article was specific to Game of Life patterns and only one example of a Garden of Eden was shown -- so the sentence made sense in that context, but it no longer seems necessary (or meaningful). If no one objects in the next week or two, I think I'll take that line out again. Dave Greene 19:02, 27 March 2007 (UTC)
Retrieved from "http://en.wikipedia.org../../../g/a/r/Talk%7EGarden_of_Eden_pattern_5eb9.html"