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In Conway's game of life, what is the shortest-known period glider gun (psudo glider guns, made from filling gaps in a glider stream do not count)? Thanks, *Max* ( talk) 02:28, 15 January 2008 (UTC).
c/12 diagonal rakes based on Corderships have been known for some time.
The first c/4 diagonal puffer was found by Hartmut Holzwart in February 2004 and is period 28; it emits tubs and beehives but some other variations have since been found. In July 2005 David Bell used it as part of a breeder, by crashing the output of a c/2 rake into it to form a sequence of switch engines:
x = 155, y = 102 77boo$77bobo$77bo$80bo$80boo$80boo$79boo$75booboo$75bo4bo$75bob4o$79b oo$79boo$79boo$81bob3o$77bobbo$76b5o6bo$76bobboo5bobo$74bobo10bo$73b3o 4bo$73bobboo$77b3o$77boo10bo$79bo8bobo3bo$77bobo8bobobbobo$70boo4boo 11bo4bo$69boo5boobo$71bo4booboobobboo$76b3obobobbobo$67boo3boobboo7bo 10bo$66boo3boo15bo6bobo3bo$68bobb3o14boo5bobobbobo$70b4o14boo6bo4bo$ 69bobo15boo$68boo13booboo$68bobo12bo4bo$67bo15bob4o14bo$68boo17boo13bo bo3bo$87boo13bobobbobo$87boo14bo4bo$89bo$85bobbo4bo$84b5o4bo$84bobboo 4bo16bo$82bobo12bo11bobo3bo$81b3o4bo7bobo10bobobbobo$81bobboo11bo12bo 4bo$85b3o$55bobo27boo$54bobbo29bo$53boo30bobo11bo17bo$52bo25boo4boo12b obo3bo11bobo3bo$51b4o22boo5boobo10bobobbobo10bobobbobo$50bo4bo6bo16bo 4booboobo8bo4bo12bo4bo$50bobbo5boobo21b3obobo$50bobbo5bo15boo3boobboo$ 51bo7bo14boo3boo$52b4obo6boo10bobb3o24bo17bo$53bo3bo4bo4bo10b4o23bobo 3bo11bobo3bo$54bo6bo15bobo25bobobbobo10bobobbobo$54b5obbo5bo8boo28bo4b o12bo4bo$61b6o9bobo$54b5o16bo$54bo21boo$53bo3bobbo24boo26bo17bo$11bobo 12boo24b4obo25bo4bo23bobo3bo11bobo3bo$10bobbo10bo4bo21bo7boboo19bo29bo bobbobo10bobobbobo$9boo7bo4bo26bobbo5bobbo6bo12bo5bo24bo4bo12bo4bo$8bo 6boobo4bo5bo20bobbo5bobbo4bobo12b6o9boo$7b6obbo7b6o21bo4bo4boo6boo5bo 20b4o$4boo7bo3b4o30b4o18bobo19booboo$3bo3b3obo4bo35bo21boo5bo14boo22bo 17bo$bbo3bo3boobobboobobbo30boo24bobo5bo31bobo3bo11bobo3bo$bbo5boo3bo 5bo6boo26bobbo22boo5bo31bobobbobo10bobobbobo$bb3o3b4obo7bobobb3o26bobo 27bobo32bo4bo12bo4bo$11bo9bo6bo57boo$bb3o6bobo7bo6bo5bo73boo$bo5bo5bo 8bo4bo4bobo3boobboobboobboobboobboobboobboobboobb3oboo27bobbo3b3o$o3b oobo3boo11boo7boo3boobboobboobboobboobboobboobboobboobb4obbo27boo6bo 10bo17bo$o3bo6b3o62boboo35bo10bobo3bo11bobo3bo$o3boobo3boo11boo7boo3b oobboobboobboobboobboobboobboobboobboo50bobobbobo10bobobbobo$bo5bo5bo 8bo4bo4bobo3boobboobboobboobboobboobboobboobboobboo34boo15bo4bo12bo4bo $bb3o6bobo7bo6bo5bo75bobbo$11bo9bo6bo80boo$bb3o3b4obo7bobobb3o78bo$bbo 5boo3bo5bo6boo50boo27bo26bo17bo$bbo3bo3boobobboobobbo54booboo25bo4bo 20bobo3bo11bobo$3bo3b3obo4bo61b4o6boo19b3o21bobobbobo10bobo$4boo7bo3b 4o58boo6boob3o41bo4bo12bo$7b6obbo7b6o59b5o$8bo6boobo4bo5bo59b3o$9boo7b o4bo95boo$10bobbo10bo4bo88boob4o16bo$11bobo12boo91b6o15bobo3bo$120b4o 16bobobbobo$141bo4bo4$148bo$147bobo3bo$147bobobbobo$148bo4bo!
Finally in October 2005 the first clean c/4 diagonal rake was constructed, by David Bell. It has period 4508 and occupies roughly a 4500 by 4000 bounding box. I think not much more than that is known about c/4 diagonal puffer and rake technology. So if you have a new period, and with a rake no less, I think it would be new and interesting. But you might want to check with Holzwart or Bell, or if you care to share your pattern here I could do so. — David Eppstein ( talk) 03:37, 15 January 2008 (UTC)
Actually, it's period 60. It emitts 1 glider every 20 generations, but it destroys 2/3 of them. It's speed is c/2. *Max* ( talk) 01:02, 16 January 2008 (UTC).
That's not a c/4 diagonal rake, it's a c/2 orthogonal rake. According to the "c/2 orthogonal spaceships, puffers, rakes" section of the Life status page I linked to above, a rake with that period is already known. — David Eppstein ( talk) 02:32, 16 January 2008 (UTC)
Let Aut(G) be the automorphism group of the finite group G. Consider the directed graph whose vertices correspond to finite groups (up to isomorphism), such that there is an edge from G to H iff . What is known about the structure of this graph? For example, are there any nontrivial cycles? Is the number of connected components finite or infinite? — Keenan Pepper 22:47, 15 January 2008 (UTC)
Sorry,If I spelled the word opinon wrong,basicilly I`m not the guy whose been posting those Physics Magazine Questions. But,I`m doing that same thing. And I`m someone,whose not doing it for the prize money just for fun.You see I`m doing The Embriodery One,what I need to know is specific examples which I wrote that show that The Embriodery One,would be sucessful.I got my own theroy,basicilly I just want a second opionon. Also,there`s some Math in this but I think I can figure that part out. —Preceding unsigned comment added by 68.161.128.203 ( talk) 23:22, 15 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 14 | << Dec | January | Feb >> | January 16 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
In Conway's game of life, what is the shortest-known period glider gun (psudo glider guns, made from filling gaps in a glider stream do not count)? Thanks, *Max* ( talk) 02:28, 15 January 2008 (UTC).
c/12 diagonal rakes based on Corderships have been known for some time.
The first c/4 diagonal puffer was found by Hartmut Holzwart in February 2004 and is period 28; it emits tubs and beehives but some other variations have since been found. In July 2005 David Bell used it as part of a breeder, by crashing the output of a c/2 rake into it to form a sequence of switch engines:
x = 155, y = 102 77boo$77bobo$77bo$80bo$80boo$80boo$79boo$75booboo$75bo4bo$75bob4o$79b oo$79boo$79boo$81bob3o$77bobbo$76b5o6bo$76bobboo5bobo$74bobo10bo$73b3o 4bo$73bobboo$77b3o$77boo10bo$79bo8bobo3bo$77bobo8bobobbobo$70boo4boo 11bo4bo$69boo5boobo$71bo4booboobobboo$76b3obobobbobo$67boo3boobboo7bo 10bo$66boo3boo15bo6bobo3bo$68bobb3o14boo5bobobbobo$70b4o14boo6bo4bo$ 69bobo15boo$68boo13booboo$68bobo12bo4bo$67bo15bob4o14bo$68boo17boo13bo bo3bo$87boo13bobobbobo$87boo14bo4bo$89bo$85bobbo4bo$84b5o4bo$84bobboo 4bo16bo$82bobo12bo11bobo3bo$81b3o4bo7bobo10bobobbobo$81bobboo11bo12bo 4bo$85b3o$55bobo27boo$54bobbo29bo$53boo30bobo11bo17bo$52bo25boo4boo12b obo3bo11bobo3bo$51b4o22boo5boobo10bobobbobo10bobobbobo$50bo4bo6bo16bo 4booboobo8bo4bo12bo4bo$50bobbo5boobo21b3obobo$50bobbo5bo15boo3boobboo$ 51bo7bo14boo3boo$52b4obo6boo10bobb3o24bo17bo$53bo3bo4bo4bo10b4o23bobo 3bo11bobo3bo$54bo6bo15bobo25bobobbobo10bobobbobo$54b5obbo5bo8boo28bo4b o12bo4bo$61b6o9bobo$54b5o16bo$54bo21boo$53bo3bobbo24boo26bo17bo$11bobo 12boo24b4obo25bo4bo23bobo3bo11bobo3bo$10bobbo10bo4bo21bo7boboo19bo29bo bobbobo10bobobbobo$9boo7bo4bo26bobbo5bobbo6bo12bo5bo24bo4bo12bo4bo$8bo 6boobo4bo5bo20bobbo5bobbo4bobo12b6o9boo$7b6obbo7b6o21bo4bo4boo6boo5bo 20b4o$4boo7bo3b4o30b4o18bobo19booboo$3bo3b3obo4bo35bo21boo5bo14boo22bo 17bo$bbo3bo3boobobboobobbo30boo24bobo5bo31bobo3bo11bobo3bo$bbo5boo3bo 5bo6boo26bobbo22boo5bo31bobobbobo10bobobbobo$bb3o3b4obo7bobobb3o26bobo 27bobo32bo4bo12bo4bo$11bo9bo6bo57boo$bb3o6bobo7bo6bo5bo73boo$bo5bo5bo 8bo4bo4bobo3boobboobboobboobboobboobboobboobboobb3oboo27bobbo3b3o$o3b oobo3boo11boo7boo3boobboobboobboobboobboobboobboobboobb4obbo27boo6bo 10bo17bo$o3bo6b3o62boboo35bo10bobo3bo11bobo3bo$o3boobo3boo11boo7boo3b oobboobboobboobboobboobboobboobboobboo50bobobbobo10bobobbobo$bo5bo5bo 8bo4bo4bobo3boobboobboobboobboobboobboobboobboobboo34boo15bo4bo12bo4bo $bb3o6bobo7bo6bo5bo75bobbo$11bo9bo6bo80boo$bb3o3b4obo7bobobb3o78bo$bbo 5boo3bo5bo6boo50boo27bo26bo17bo$bbo3bo3boobobboobobbo54booboo25bo4bo 20bobo3bo11bobo$3bo3b3obo4bo61b4o6boo19b3o21bobobbobo10bobo$4boo7bo3b 4o58boo6boob3o41bo4bo12bo$7b6obbo7b6o59b5o$8bo6boobo4bo5bo59b3o$9boo7b o4bo95boo$10bobbo10bo4bo88boob4o16bo$11bobo12boo91b6o15bobo3bo$120b4o 16bobobbobo$141bo4bo4$148bo$147bobo3bo$147bobobbobo$148bo4bo!
Finally in October 2005 the first clean c/4 diagonal rake was constructed, by David Bell. It has period 4508 and occupies roughly a 4500 by 4000 bounding box. I think not much more than that is known about c/4 diagonal puffer and rake technology. So if you have a new period, and with a rake no less, I think it would be new and interesting. But you might want to check with Holzwart or Bell, or if you care to share your pattern here I could do so. — David Eppstein ( talk) 03:37, 15 January 2008 (UTC)
Actually, it's period 60. It emitts 1 glider every 20 generations, but it destroys 2/3 of them. It's speed is c/2. *Max* ( talk) 01:02, 16 January 2008 (UTC).
That's not a c/4 diagonal rake, it's a c/2 orthogonal rake. According to the "c/2 orthogonal spaceships, puffers, rakes" section of the Life status page I linked to above, a rake with that period is already known. — David Eppstein ( talk) 02:32, 16 January 2008 (UTC)
Let Aut(G) be the automorphism group of the finite group G. Consider the directed graph whose vertices correspond to finite groups (up to isomorphism), such that there is an edge from G to H iff . What is known about the structure of this graph? For example, are there any nontrivial cycles? Is the number of connected components finite or infinite? — Keenan Pepper 22:47, 15 January 2008 (UTC)
Sorry,If I spelled the word opinon wrong,basicilly I`m not the guy whose been posting those Physics Magazine Questions. But,I`m doing that same thing. And I`m someone,whose not doing it for the prize money just for fun.You see I`m doing The Embriodery One,what I need to know is specific examples which I wrote that show that The Embriodery One,would be sucessful.I got my own theroy,basicilly I just want a second opionon. Also,there`s some Math in this but I think I can figure that part out. —Preceding unsigned comment added by 68.161.128.203 ( talk) 23:22, 15 January 2008 (UTC)