Timeline for Conway's game of life for random initial position
Current License: CC BY-SA 3.0
27 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 13, 2017 at 12:32 | history | edited | CommunityBot |
replaced http://cstheory.stackexchange.com/ with https://cstheory.stackexchange.com/
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| Jan 3, 2014 at 6:08 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Jun 11, 2013 at 23:12 | answer | added | Vincent Beffara | timeline score: 4 | |
| Jun 11, 2013 at 14:46 | answer | added | Heijne | timeline score: 3 | |
| Jun 11, 2013 at 14:22 | history | edited | Gil Kalai |
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| Jun 7, 2013 at 23:32 | answer | added | helper | timeline score: 0 | |
| Jun 6, 2013 at 21:36 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Jun 5, 2013 at 22:41 | answer | added | ACW | timeline score: 15 | |
| Jun 5, 2013 at 18:26 | comment | added | Joel David Hamkins | Ah, I see you mention this version in your question over at the other site. | |
| Jun 5, 2013 at 18:03 | comment | added | Joel David Hamkins | Gil, regarding your "noisy" adaptation, it would also be natural to modify the game of life rules to be a probabilistic function of the neighboring cells, rather than a deterministic one. Thus, the likelihood that a cell turns on or off would be affected by it's current neighbors. For example, perhaps cells surrounded by 8 live cells have very little chance of still living, but those surrounded by only 4 have a greater chance (whereas in the deterministic version they definitely die), and cells with 1 live neighbor have a greater chance of spontaneous life than those with 0 live neighbors. | |
| Jun 5, 2013 at 17:54 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Jun 3, 2013 at 19:08 | answer | added | André Henriques | timeline score: 4 | |
| Jun 2, 2013 at 14:15 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Jun 1, 2013 at 0:23 | comment | added | fedja | >so whatever that probability is then it'll be small< Let's say about $1−(1−(p^{20})(1−p)^{180})^{n^2/200}$. (I was too lazy to count the cells but you get the idea) Now here is the difference between a mathematician and a normal person. The mathematician believes that it is 1 and the normal person that it is 0. All existing computers are normal people, which makes it extremely hard to use them to do mathematics of this type... | |
| May 31, 2013 at 19:23 | comment | added | Andrew Stacey | @André Only on a mathematics forum could one argue that experimentation was no basis for assertion! Actually, I've yet to see a glider gun in my simulations so whatever that probability is then it'll be small. I suspect that it might be because it's on a torus so any glider gun that forms has a distinct possibility of shooting itself. | |
| May 31, 2013 at 19:15 | answer | added | David Eppstein | timeline score: 24 | |
| May 31, 2013 at 15:39 | comment | added | André Henriques | @Andrew Stacey: It is rather naive to base an answer on experimentation. For example, there is a positive probability that somewhere in your system (lets take it to be infinite) you'll encounter this: en.wikipedia.org/wiki/File:Gospers_glider_gun.gif | |
| May 31, 2013 at 14:35 | answer | added | j.c. | timeline score: 23 | |
| May 31, 2013 at 14:21 | comment | added | Algernon | @Allen: well, your question is surely interesting, but I don't see it anywhere in the OP's question. There is a wealth of interesting questions one can ask about the behavior of a cellular automaton on random initial configurations. Why e.g. not asking whether with positive probability every cell eventually dies out, which is more in the spirit of bootstrap percolation? | |
| May 31, 2013 at 13:27 | comment | added | Allen Knutson | @Algernon: does it with positive probability settle down to a 2-periodic state? Stronger: is there a fixed time N for which this is true? | |
| May 31, 2013 at 13:13 | comment | added | Boris Bukh | Game of Life supports universal Turing machine that can even have self-replicating function. The Turing machine can run arbitrarily intelligent program. So, a question is "will the Game of Life universe with random initial position be filled with super-intelligent life forms, or will the chaos reign". I abstain from defining the meaning of "intelligent" :-) | |
| May 31, 2013 at 12:10 | comment | added | Algernon | Could you perhaps be more specific about what you want to know about the behavior of the game of life with random initial configuration? | |
| May 31, 2013 at 12:05 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Corrected spelling.
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| May 31, 2013 at 11:39 | comment | added | Andrew Stacey | My experiments with GoL on a torus show that it eventually stabilises to a steady-state (modulo the alternating cross). You can see a video of one run at youtube.com/watch?v=tZTIiKcqdtI (the background is the same as what's happening on the torus). | |
| May 31, 2013 at 11:09 | comment | added | André Henriques | Very interesting question. Presumably, something chaotic (like Brian's Brain), but with a much smaller density of gliders. | |
| May 31, 2013 at 10:39 | history | asked | Gil Kalai | CC BY-SA 3.0 |
