Comments on: Longest-Lived Soup Density in Conway’s Game of Life http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/ A blog of recreational math and coding Sat, 31 Jul 2010 00:05:34 -0400 http://wordpress.org/?v=2.8.4 hourly 1 By: Nathaniel Johnston » The Maximal Lifespan of Patterns in Conway’s Game of Life http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/comment-page-1/#comment-921 Nathaniel Johnston » The Maximal Lifespan of Patterns in Conway’s Game of Life Fri, 31 Jul 2009 12:29:52 +0000 http://www.nathanieljohnston.com/?p=418#comment-921 [...] a couple of recent posts, I argued that random patterns in Conway’s Game of Life tend, on average, to [...] [...] a couple of recent posts, I argued that random patterns in Conway’s Game of Life tend, on average, to [...]

]]> By: Nathaniel Johnston » Longevity in Conway’s Game of Life Revisited http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/comment-page-1/#comment-613 Nathaniel Johnston » Longevity in Conway’s Game of Life Revisited Fri, 17 Jul 2009 12:01:43 +0000 http://www.nathanieljohnston.com/?p=418#comment-613 [...] couple of weeks ago, I posted some intuition that suggested that, in Conway’s Game of Life, the longest-lived patterns [...] [...] couple of weeks ago, I posted some intuition that suggested that, in Conway’s Game of Life, the longest-lived patterns [...]

]]> By: Nathaniel Johnston » The Online Life-Like CA Soup Search http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/comment-page-1/#comment-551 Nathaniel Johnston » The Online Life-Like CA Soup Search Sat, 11 Jul 2009 18:34:00 +0000 http://www.nathanieljohnston.com/?p=418#comment-551 [...] I mentioned in this post, one way to learn about the general behaviour of Conway’s Game of Life (or any other [...] [...] I mentioned in this post, one way to learn about the general behaviour of Conway’s Game of Life (or any other [...]

]]> By: Nathaniel http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/comment-page-1/#comment-471 Nathaniel Sun, 28 Jun 2009 16:11:43 +0000 http://www.nathanieljohnston.com/?p=418#comment-471 <a href="#comment-465" rel="nofollow">@Elithrion</a> - Haha yeah, I actually had already written the script and started the computations when you made the suggestion. Great minds think alike, I guess ;) You make a good point about the median vs. mean thing - I'll definitely create median data if/when I post the results of the toroidal version of this script. And I completely meant to attach the source code to this post (as I try to do with all my coding posts), but I forgot and it unfortunately is sitting on a harddrive halfway around the world right now. I'll update the post to include the source code in two weeks time ;) Also, just as an FYI in case you're curious - I tried something semi-similar to what you described about trying to create methuselahs based on observing past long-lived patterns and evolving the density used. Instead I tried things like taking the top half of one methuselah (possibly modified by one or two cells) and the bottom half of another methuselah (also possibly mutated a bit) and checked whether that was long-lived. It was basically a standard cross-breed and mutate genetic algorithm, but unfortunately it yielded results that were no better than a uniformly random search, due to the high volatility of methuselahs. Silly Life. @Elithrion – Haha yeah, I actually had already written the script and started the computations when you made the suggestion. Great minds think alike, I guess ;)

You make a good point about the median vs. mean thing – I’ll definitely create median data if/when I post the results of the toroidal version of this script.

And I completely meant to attach the source code to this post (as I try to do with all my coding posts), but I forgot and it unfortunately is sitting on a harddrive halfway around the world right now. I’ll update the post to include the source code in two weeks time ;)

Also, just as an FYI in case you’re curious – I tried something semi-similar to what you described about trying to create methuselahs based on observing past long-lived patterns and evolving the density used. Instead I tried things like taking the top half of one methuselah (possibly modified by one or two cells) and the bottom half of another methuselah (also possibly mutated a bit) and checked whether that was long-lived. It was basically a standard cross-breed and mutate genetic algorithm, but unfortunately it yielded results that were no better than a uniformly random search, due to the high volatility of methuselahs. Silly Life.

]]> By: Elithrion http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/comment-page-1/#comment-468 Elithrion Sun, 28 Jun 2009 04:11:58 +0000 http://www.nathanieljohnston.com/?p=418#comment-468 Actually, (apologies for the double-post) could you send me the source for this? I'm curious to tweak it a little - I want to see if I can make it vary probabilities cell-by-cell and either come up with a more efficient generation mechanism this way (I imagine that having a few clumps separated by some white space will yield higher maximums than a uniform distribution, for example), or see if I can tweak it to evolve towards methuselahs (by having it continuously adjust the probabilities towards whatever gets the best results). Admittedly the latter option is unlikely due to high sensitivity of the generations to the exact starting conditions, but it would be awesome if it worked (and the former option could work if it doesn't) :D Actually, (apologies for the double-post) could you send me the source for this? I’m curious to tweak it a little – I want to see if I can make it vary probabilities cell-by-cell and either come up with a more efficient generation mechanism this way (I imagine that having a few clumps separated by some white space will yield higher maximums than a uniform distribution, for example), or see if I can tweak it to evolve towards methuselahs (by having it continuously adjust the probabilities towards whatever gets the best results). Admittedly the latter option is unlikely due to high sensitivity of the generations to the exact starting conditions, but it would be awesome if it worked (and the former option could work if it doesn’t) :D

]]> By: Elithrion http://www.nathanieljohnston.com/index.php/2009/06/longest-lived-soup-density-in-conways-game-of-life/comment-page-1/#comment-465 Elithrion Sun, 28 Jun 2009 01:06:48 +0000 http://www.nathanieljohnston.com/?p=418#comment-465 Ah, you sort of took my request! Although I think more extensive data would be nice - median density seems like it might be a bit more representative than average, and maximum density would be nice to have for the actual search (although that might need checks for outliers). Of course, it's not unlikely that the graphs for those would just mirror the average one, but then again there's a decent chance they would not (in particular, I expect that they would differ with regards to the 90% hump at least), and that would be interesting too. Ah, you sort of took my request! Although I think more extensive data would be nice – median density seems like it might be a bit more representative than average, and maximum density would be nice to have for the actual search (although that might need checks for outliers). Of course, it’s not unlikely that the graphs for those would just mirror the average one, but then again there’s a decent chance they would not (in particular, I expect that they would differ with regards to the 90% hump at least), and that would be interesting too.

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