gameoflifemaniac wrote:How do you define a cluster?
,A methuselah is a pattern that takes a large number of generations in order to stabilize (known as its lifespan) and becomes much larger than its initial configuration at some point during its evolution.
x = 220060, y = 65, rule = B3/S23
40002b2o60018b2o19978b2o30001b2o19995b2o$2o9998b2o9998b2o9999b2o9998bo
10012b2o10009b2o10000b2o9971b3o9997b3o10018bo9982b3o9994bo10032b3o
10009b3o9955bo10001bo9994bo10017bo10003bo10008bo10021bo10004bo$o9999bo
9999bo10000bo9999bo10012bo10010bo10001bo29993bo19979bo30002bo10001bo
9994bo10017bo10003bo9978b2o28bo10021bo10004bo$40001bo60019bo19979bo
30002bo10001bo9994bo10017bo10003bo9977bo30bo10021bo10004bo$200001bo$
20b2o199979bo$19bo179982b2o$19bo59982b2o49998b2o69997bo$19bo59981bo
49999bo69999bo$60001bo49999bo69999bo$60001bo49999bo5$170010bo$40008b2o
130000bo$40008bo130001bo5$90030b2o$90029bo$90029bo$90029bo6$160002b2o$
160001bo$160001bo$20014b2o139985bo$20013bo$20013bo$20013bo60046b2o$
80059bo$10017b2o19983b2o50055bo19940b3o$10016bo19984bo50057bo69940bo$
10016bo19984bo119998bo$10016bo19984bo119998bo2$70002b2o$70001bo50007b
3o$50002b2o19997bo$50001bo19999bo$50001bo80000b2o9998b2o$50001bo79999b
o9999bo79999bo$130001bo9999bo79999bobo$130001bo9999bo79998b2o2$190002b
2o$190001bo$190001bo$190001bo5$210002b2o$210001bo$210001bo$210001bo!
NickGotts wrote:Here's the first post that reports an interesting finding. (Interesting to me, anyway!)
...
The rle above shows 23 eight-cell patterns which take more than 8192 steps (I tend to use powers of 2) to stabilise.
dvgrn wrote:Huh, so these methuselahs fall into an apparently unsearched gap between the space of all 8-cell single clusters (Tomas Rokicki's search from 2005, which found 7468M as the longest-lasting methuselah in that category) and the space of all 8-cell Patterns That Can't Be Subdivided Into Two Or More Parts That All Stabilize Separately Before Interacting.
(A shorthand word might be good to have, for that second category...)
x = 6, y = 34, rule = B3/S23
5bo$5bo$5bo28$b2o$o$o$o!
danny wrote:The longest lasting pattern there is this, 14321M:Code: Select allx = 6, y = 34, rule = B3/S23
5bo$5bo$5bo28$b2o$o$o$o!
It even has a mango in its ash!
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
x = 8007, y = 28005, rule = Life
o4000$o$o$o3998$3o3997b2o$2bo3999bo$bo4000bo$4002bo3997$o3999bo$o4000b
2o$ob2o3999b2o$bo4000bo3997$obo3997bobo3998bo2b3o$bo3999bo3998bo2bo$bo
4000bo3998bo$b2o4000b2o$o4004bo3996$3o$3bo$bo$2b3o3997$3o2bobo$o5bo$bo
4bo$6b2o$5bo3996$obo3bobo$bo5bo$bo5bo$2o5b2o$2bo3bo!
x = 39, y = 24, rule = B3/S23
19bo$12b2o5bo5b2o$14bo4bo4bo$4b2o27b2o$3bobo6b2obo7bob2o6bobo$4bo8bob
2o5b2obo8bo$12b2o11b2o$12b2o11b2o$6bo5b2o11b2o5bo$5b3o8bo5bo8b3o$4bobo
bo3bob2o7b2obo3bobobo$4bo3b4ob4o5b4ob4o3bo$2b2o6b2o2bob2o3b2obo2b2o6b
2o$bo4bo4bob5o3b5obo4bo4bo$3o2bobo4b2obob2ob2obob2o4bobo2b3o$bo4bo3b2o
3bob2ob2obo3b2o3bo4bo$2b2o5b2o2bo3b2ob2o3bo2b2o5b2o$4bo3bo7bo5bo7bo3bo
$4bobobo7bo5bo7bobobo$5b3o3bo15bo3b3o$6bo6bo11bo6bo$10b2o15b2o$10b2obo
11bob2o$12b2o11b2o!
x = 8, y = 3, rule = B3/S23
6bo$2o$bo3b3o!
x = 10, y = 13, rule = B3/S23
3b2o2$bo2$obobo$b4o$b2o$2b4o2b2o$2b2ob2o2bo$b3o2b3o$bo2b4o$bo2b2o$2b3o
!
x = 15, y = 4, rule = B3/S23
13bo$3o9bobo$obo9bobo$obo9bobo!
Since all velocities will be integer ratios, you might want to use that instead of angle in degrees, to avoid future problems specifying knightship velocities.
Or, since all known small spaceships travel in only 8 directions, maybe a compass rose (N, NE, etc) or even radians with the (pi/4) implied.
x = 8007, y = 28005, rule = Life
o4000$o$o$o3998$3o3997b2o$2bo3999bo$bo4000bo$4002bo3997$o3999bo$o4000b
2o$ob2o3999b2o$bo4000bo3997$obo3997bobo3998bo2b3o$bo3999bo3998bo2bo$bo
4000bo3998bo$b2o4000b2o$o4004bo3996$3o$3bo$bo$2b3o3997$3o2bobo$o5bo$bo
4bo$6b2o$5bo3996$obo3bobo$bo5bo$bo5bo$2o5b2o$2bo3bo!
As an id for a methuselah I suggest the pattern with maximum population (until time to stability), in case of a tie - just breaking it e.g. by the first occurring maximum
NickGotts wrote:2718281828 says:As an id for a methuselah I suggest the pattern with maximum population (until time to stability), in case of a tie - just breaking it e.g. by the first occurring maximum
I haven't looked much at intermediate cell-counts, but that's a perfectly sound measure. However, I think the problem with "methusaleh" is that it's just an ill-defined term. There are several ways it could be defined precisely, of which you suggest one, but no particular reason I can see for preferring one over another.
x = 47, y = 26, rule = B3/S23
24bo$22bobo$23b2o13$2bo$obo$b2o2$3b4o33b4o$2b6o31b6o$b8o29b8o$2o6b2o
27b2o6b2o$b8o29b8o$2b6o31b6o$3b4o33b4o!
x = 2040028, y = 300076, rule = B3/S23
o39999bo40000bo39998b3o39997b3o39997b4o39996b4o40001bo39994bo40001bo
39999bo39997bo39999bo39999bo$o39999bo39999b3o39997bo40002bo39996bo3bo
39995bo39999bo40003bo39995b2obo39996b2obo40001bo39995bo5bo39993bo$obo
39997bobo39997bo2b2o39998b2o39998bo39996bo39999bo3bo39995bobob2o39994b
2ob2o39997bo40001bo39995b2obobo39996bo39999bo4bo$4bo40000bo39996bo
40002bo39998b2o39995bo39999bo40001bo40001bo39998b3o39994bo2bo39997bo
40000b4o39996b4o$2b3o39997b3o79999bo40001bo119995bo39999bo80003bo
39997bo59996$o3bo39995bo39999bo39999b3o2bo39994b3o2bo39994bo39999bo
39999bo39999bo39999bo2b3o39994bob2o39996bo2b3o39996bo39999bo39999bo
39999bo39999bo39999b2o39999bo39997bo3bo39995bo39999bo39999bo39999bo
39999bo$obo39997bobo39997bobo39997bo2bo39996bo2bo39997b2o2bo39994bobo
39997bobo39997bobo39997bo3bo39999bo39997bobo39995bobo39997bobo39997bob
o39997bobo39997bobo39997bo39999bobo39998bobo39996bobo39997bobo39997bob
o39997bobo39997bobo$o2bo40002bo79994bobo39999bo39996bo2bo159998b2o
39996bo2b3o39994bo2bo40002bo199995bo39999bo39997bo2bo160002bo$3bo
39998bobo39997bobobo79994bo39999bobo39998bob2o39996bobobo39995bobo
159997bobo39997bobobo39995bob2o39996bobobo39995bobo39997bo80001bo
39997bob2o39996bobobo39995bobo39997bobo39997bobobo$bo40003bo39999bo
160000bo39998bo39999b2o159998bo39999bo40000bo39998bo39999b2o39997b3o
39995bob3o39995bo40003bo39998bo39999b2o39998bo39999bo$40004bo39999bo
159998bo39999bo39999bo160000bo39999bo39998bo39999bo39999bo159999bo
39999bo39999bo40000bo39999bo59995$24b3o39983b3o39987b2o39998b2o80001b
2o79999b2o39994b3o39997b3o39997b2o40015bo39982b2o40006bo39993b2o39997b
o120008b2o39989bo$2o22bo2bo39982bo2bo39986bo39999bo80002bo80000bo
39995bo2bo39996bo2bo21b2o39973bo40015b2obo39980bo40006b2obo39991bo
39997b2obo120006bo39989b2obo$o360024bo39991bo39999bo79990bo79992bo
159999bo$400016b2obo39980b2o40006bo$400017bo39982bo40006b2obo39989b2o$
480008bo39991bo3$80003b3o199994b3o$40000b2o40001bo2bo199993bo2bo40007b
2o$40000bo280010bo399989bo$720000b2obo40006b2o$720001bo40008bo5$
120002b3o79995b3o$120002bo2bo79994bo2bo6$560001bo$560000b2obo39998b2o$
560001bo40000bo59974$3o39997b3o40007b3o39996b3o39988b3o40003b3o39991b
3o40001b3o39993b3o40005b3o39989b3o39997b3o40009b3o40001b3o39997b3o
39981bo40012bo39986b3o39997b3o39997b3o39997b3o39997b3o40004b3o40009b3o
40000b3o39975bo40004bo$80010bo2bo39995bo2bo79993bo2bo119990bo2bo79996b
o2bo39996bo2bo120012bo2bo39980bo40012bo39986bo2bo319996bo40004bo$
600000bo40012bo359986bo40004bo$560000bo120017bo39999bo$560000bo120017b
o39998b2obo$560000bo120017bo39999bo159982bo$880000b2obo$200000b3o
120003b3o480002bo79989bo$16b3o519981b3o280007b2obo159987bo$16bo2bo
519980bo2bo280007bo119989bo39998b2obo$160008b3o199989b3o559997b2obo
39997bo$160008bo2bo199988bo2bo400009bo159987bo$40012b3o439985b3o
280009b2obo239997bo$40012bo2bo439984bo2bo280009bo239998b2obo$600011b3o
39986b3o360010bo$600011bo2bo39985bo2bo200005bo$840008b2obo$240004b3o
39993b3o560006bo199991bo$240004bo2bo39992bo2bo759996b2obo$80000b3o
360007b3o599988bo3$120000b3o280006b3o59978$120012bo39987b2o39998b2o
39998b2o39998b2o120008b2o39988bo80020b2o120005b2o40001b2o39999b2o
40011b2o$120012b3o39985bo39999bo39999bo39999bo120009bo39989b3o80018bo
120006bo40002bo40000bo40012bo$120000b2o11bo319987bo$120000bo8$440011b
2o$440011bo279988bo$720000b3o$720001bo14$160011bo79998bo$160011b3o
79996b3o$160012bo79998bo2$520000bo$520000b3o$520001bo5$400000bo$
400000b3o$400001bo$200010bo439989bo$200010b3o439987b3o$200011bo439989b
o4$760000bo$760000b3o$760001bo2$280009bo$280009b3o$280010bo7$680000bo$
680000b3o$680001bo59937$80000b3o79997b3o39997b3o39997b3o40006bo39990b
3o39997b3o39998b3o79996bo39999bo80011b3o39985bo40018b3o40005b3o40000b
3o39999b3o80001b3o39998b3o40002b3o39955bo80051b3o39983bo39993bo39967bo
40011bo39987bo39999bo40008bo39990bo40004bo39994bo79999bo40003bo79995bo
119999bo40018bo80001bo39999bo80005bo$280009b3o199988b3o39997b3o119997b
3o359997b3o120035b3o39991b3o39965bo40011b3o39985bo39999bo40008b3o
39988bo40004b3o39992bo79999b3o40001bo79995b3o119997b3o40016bo80001bo
39999bo80005bo$200010bo79999bo199990bo39999bo119999bo359999bo120037bo
39993bo39966bo40012bo39986bo39999bo40009bo39989bo40005bo39993bo80000bo
40002bo79996bo119999bo40017bo80001bo39999bo80005bo$200010b3o$200011bo
319997b3o1280004bo$1000042b3o799971bo$1560002bo240013bo$1560002bo$
1560002bo$400000bo$400000b3o$400001bo$1680008bo$1680008bo$1680008bo2$
800000bo1239999bo$800000b3o79997bo39999bo1119999b3o$800001bo79998b3o
39997b3o1119998bo$880001bo39999bo$80028bo$80028b3o1279969bo$80029bo
1279970bo$1360000bo2$1240000bo$240009bo79994bo919995bo$160011bo79997b
3o79992b3o919993bo$160011b3o79996bo79994bo1000004bo$160012bo439987bo
680009bo39999b3o$600000b3o600010bo79996b3o39998bo$600001bo600011b3o
79995bo$1200014bo239985bo$480008b3o160007b3o319979bo440004bo39994bo$
960000b3o440002b3o39992bo$280000b3o679998bo440004bo199993bo$1600000b3o
$1600001bo4$680000bo$680000b3o$680001bo399998bo400002bo$760000bo
319999b3o400000b3o$760000b3o319998bo79998bo320003bo$760001bo399998bo$
1160000bo679999bo$1840000b3o$1840001bo119998bo$1960000b3o$360002bo
759997bo840000bo$360002b3o759995bo$360003bo759996bo9$720000bo$720000b
3o$720001bo9$1920000bo$1920000b3o$1920001bo!
x = 181, y = 312, rule = B3/S23
178bo$178b3o$179bo23$166bo$166bo$166bo273$25bo$25bo$25bo6$o$o$o$o!
x = 227, y = 43, rule = Life
o3bo16bo19bo19bo18b5o15bo5bo$obobo20bo18b2o18bo15bo3bo16b2ob2o$o3bo15b
ob3o15bob2o16bob2obo37bo2$21bo20bo19bo36$2o2b2o14b2o2bobo13b2o2bo15bob
ob2o14bobobobo13bobobo15bobo2bo15b2ob2o15b2obo16b2o2bo15bo2bo17bobo$2b
o3bo15bo2bo16bo2b2o14bo4bo14bo3bo15bo3b2o14bo2bobo13bo5bo13bo4b2o13bo
3bobo13bobo2b2o13b2o3b2o$3bo19bo19bo19bo19bo19bo19bo19bo19bo19bo19bo
19bo!
x = 4, y = 10, rule = Life
2bo2$b3o5$b3o2$2bo!
NickGotts wrote:2718281828,
I have to admit I don't quite understand your definition of a "methusaleh" - I'm not sure I could apply it to decide whether a given pattern is a "methusaleh", or which of two "methusalehs" is more methusalehish. Usually, they are described in terms of the number of steps to stability rather than maximum size. But in any case, I see no point in arguing about definitions of a class I've never found very interesting!
x = 22, y = 4, rule = LifeHistory
20.A$3A16.A.A$A.A16.A.A$A.A16.A.A!
x = 263, y = 91, rule = B3/S23
14$78b3o$22b3o52bo2bo$21bo2bo3$245b3o$76bo90b3o75bo2bo$20b2o54b2o89bo
2bo$20bo3$244bo$165b2o76b2o$165bo47$23b3o$22bo2bo140b3o$166bo2bo$252b
3o$85b3o164bo2bo$84bo2bo$21b2o$22bo141bo$164b2o$250b2o$84bo166bo$83b2o
!
x = 909, y = 776, rule = B3/S23
54b2o$54bobo$54bo271$427b2o$427b2o6$460bo$459bo2bo$459bo2bo6bo$446bo
14bo6bobo$445bobo20bobo$446bo22bo5$428bo$427bobo21b2o10b2o$427bobo20bo
2bo9b2o$428bo12bo8bobo$440bobo8bo$423b2o7b2o5bo2bo$422bo2bo5bo2bo5b2o$
423b2o7b2o$451bo$428bo21bobo$427bobo19bo2bo$406bo20bobo20b2o$405bobo
20bo35b2o$406b2o55bobo$410b2o52bo$409bobo39b2o49b2o$410bo40b2o49bobo$
503b2o$462bo$426b2o34bo$394bo31b2o34bo$393bobo49b2o37b2o$394b2o49b2o
17b2o18b2o$464b2o$439bo$439bo52b2o$439bo52b2o2$434bo$434bo16b2o$434bo
16b2o$403bo$402b2o$401bo$403b5o$400b5o2bo$401bo41bo$405b2o35bobo$425b
2o14bo3bo$404b3o17bobo14bo4b3o$403b2o2bo17bo15b2ob2o2bo$404bo2bo21b2o
4bob2obo3bob2o$405b2o21bo2bo4b6o$428bob2o7bo3bo$428b2o2b2ob2o9b2o$427b
2ob4ob2ob2obo6bo$404bo21bob4obo4bo2bo5bo$403bobo19b3obo2bo4b9o$402bo
23bobo3bo4bo4bo2bo$406bo20b2o3bo5b2o4bo5bo$394b3o9bo12b2o12bo8bo2bo4b
2o$394bo3bo3bobobo3b3o6b2o21b4o6bo5b3o$394b4o5bo13b3o21b2o4b2o9bo3bo
21b2o$412bo4b3o22bob6o8bo4bo20b2o3b2o$404bo2bo6bobo3bo25b2o7bo3b2o2bo
25b2o$404bo9bob2o2bo28b2o4bo3bo3bo$414b3o9b2o29b3ob2o$407b5o4b4o8bo26b
obo$420bo4bo2bo26bob3o8b3o$410bo6bob2o6bo$408bob2o5bo2b2o3b2o12b2o$
401b3o3bo2bo6bobo2bo15bo2bo$400bo2b3o2b3o10bobo15bobo$404b2obobo11bo2b
o3bo11bo51bo$400b3o2bo2bo7b3ob6o3bo2b2o57bobo$402b2ob2ob2obo4b2o3bob2o
6bo2bo56b2o$403bobo3bobo8bo6b2o2b3o$402b3o9b2o5b3o8b2o17bo$402b2obo7b
3o8b2o25bo$403b4o4b3obo35bo$402bo3bo4b2o9b2obo63b2o$402bob2o5b2o2b3o5b
2ob2o7b2o52b2o$402bobo10b2o6b2obo7bobo$403bo8bo2b2o3bo4bo9bo49b3o$413b
3o3b2o$414bo3b2obo61bo5bo$419bobo61bo5bo$420b2o4bo56bo5bo2$485b3o2$
483bo$406b2o17b2o55bobo10b2o$406b2o17b2o55bobo10b2o$483bo2$405b2o$405b
2o2$466b2o$422b2o42bobo$421bo2bo42bo$422b2o$442b3o28b3o2$419b2o37b2o$
419b2o37b2o2$449b2o19b2o$449b2o19b2o$435b3o$440bo$439bobo$439bobo$401b
o15b2o21bo$401bo15b2o$401bo42b2o$443bo2bo$444b2o5$423b2o$423b2o6$424b
3o5$410b2o$410b2o$428b2o$428b2o$421b2o$421b2o119$279bo$277b2o$278b2o
207$907bo$908bo$906b3o23$2bo$2o$b2o!
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