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Largest and oldest methuselah ever found!

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Largest and oldest methuselah ever found!

Postby TDiff? » January 16th, 2018, 7:55 am

OMG GUYS!

I just found a crasy thing.
A methuselah that lives for more than 2 MILLION GENERATIONS without being stable!!

Check this out :
x = 73, y = 84, rule = B3/S23
26bo3b2o2b2obo$26bo3b2o4bob2o$26bo3b2o2b2ob2o$30b2o$28bo2bo$28bobo17b
2o$29bo18b2o7$56b2o$46bo9b2o$45bo2bo$44bo4bo$29b2o2b5o6bo4bo$29bo7bo6b
o4b3o$29bo4bob2o7bobob2o$33b3o10bobo$48bo2bo$49b2o19$57b2o$56bo8bo$56b
o8bo$57b2ob2ob2o$59bo2bo$59bo2bo$60b2o7$o3b2o2b2obo$o3b2o4bob2o$o3b2o
2b2ob2o$4b2o$2bo2bo$2bobo17b2o$3bo18b2o$41bo3b2o2b2obo$41bo3b2o4bob2o$
41bo3b2o2b2ob2o$45b2o$43bo2bo$43bobo$30b2o12bo$20bo9b2o$19bo2bo$18bo4b
o$3b2o2b5o6bo4bo$3bo7bo6bo4b3o$3bo4bob2o7bobob2o$7b3o10bobo48b2o$22bo
2bo12b2o21bo9b2o$23b2o13b2o20bo2bo$59bo4bo$44b2o2b5o6bo4bo$10b2o32bo7b
o6bo4b3o$10b2o32bo4bob2o7bobob2o$35b2o11b3o10bobo$35b2o26bo2bo$64b2o!


Right now i'm trying to simplify the pattern to make it smaller :D
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Re: Largest and oldest methuselah ever found!

Postby Bullet51 » January 16th, 2018, 8:30 am

Crazier: (found in Golly's pattern collection)
# ark2 -- 19 cells, stabilizes at 8120878 gens, found by Nick Gotts.
x = 53, y = 44, rule = B3/S23
50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!


It may be more challenging to find a pattern like this but eventually resolves into still lifes, oscillators and spaceships. Such a pattern may produce a SE-ward glider by ash-hitting (as your pattern demonstrates), and destruct the switch engines eventually.
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Re: Largest and oldest methuselah ever found!

Postby TDiff? » January 16th, 2018, 8:32 am

Bullet51 wrote:Crazier: (found in Golly's pattern collection)
# ark2 -- 19 cells, stabilizes at 8120878 gens, found by Nick Gotts.
x = 53, y = 44, rule = B3/S23
50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!


It may be more challenging to find a pattern like this but eventually resolves into still lifes, oscillators and spaceships. Such a pattern may produce a SE-ward glider by ash-hitting (as your pattern demonstrates), and destruct the switch engines eventually.

AAAAAAh!

Why isn't this one shown here : http://www.conwaylife.com/w/index.php?t ... ethuselahs ??
lol
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Re: Largest and oldest methuselah ever found!

Postby dvgrn » January 16th, 2018, 8:42 am

TDiff? wrote:
Bullet51 wrote:Crazier: (found in Golly's pattern collection)
# ark2 -- 19 cells, stabilizes at 8120878 gens, found by Nick Gotts.
x = 53, y = 44, rule = B3/S23
50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!


It may be more challenging to find a pattern like this but eventually resolves into still lifes, oscillators and spaceships. Such a pattern may produce a SE-ward glider by ash-hitting (as your pattern demonstrates), and destruct the switch engines eventually.

AAAAAAh!

Why isn't this one shown here : http://www.conwaylife.com/w/index.php?t ... ethuselahs ??
lol

Short answer: it's too big.

Longer answer: 40514M is kind of an exception that maybe shouldn't really be in the list -- anyone who spends enough time decorating an existing methuselah with a scattering of late-reacting blinkers or blocks can find more large-bounding-box methuselahs along these same lines.

Minimizing the population rather than the bounding box gives a lot of options along the lines of your two-switch-engine ark. For many more examples, see Nick Gotts' blog from the early days of blogging. None of these are in the methuselah list either, and probably shouldn't be put there, more or less for the same reason of large bounding box size... but maybe it would be good to add a link to that page!
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Re: Largest and oldest methuselah ever found!

Postby TDiff? » January 16th, 2018, 8:46 am

dvgrn wrote:
TDiff? wrote:
Bullet51 wrote:Crazier: (found in Golly's pattern collection)
# ark2 -- 19 cells, stabilizes at 8120878 gens, found by Nick Gotts.
x = 53, y = 44, rule = B3/S23
50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!


It may be more challenging to find a pattern like this but eventually resolves into still lifes, oscillators and spaceships. Such a pattern may produce a SE-ward glider by ash-hitting (as your pattern demonstrates), and destruct the switch engines eventually.

AAAAAAh!

Why isn't this one shown here : http://www.conwaylife.com/w/index.php?t ... ethuselahs ??
lol

Short answer: it's too big.

Longer answer: 40514M is kind of an exception that maybe shouldn't really be in the list -- anyone who spends enough time decorating an existing methuselah with a scattering of late-reacting blinkers or blocks can find more large-bounding-box methuselahs along these same lines.

Minimizing the population rather than the bounding box gives a lot of options along the lines of your two-switch-engine ark. For many more examples, see Nick Gotts' blog from the early days of blogging. None of these are in the methuselah list either, and probably shouldn't be put there, more or less for the same reason of large bounding box size... but maybe it would be good to add a link to that page!


Thanks for your answers!
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Re: Largest and oldest methuselah ever found!

Postby NickGotts » January 17th, 2018, 6:45 am

I should do something about that old blog! For one thing, I didn't quite understand what a blog is supposed to be, so it's really just a website on which I've plonked various patterns. Maybe I should repost them on ConwayLife. TDiff's pattern is interesting in that the backward stream of gliders runs between the two switch engines, but otherwise much like many of the ones I found, and eventually stabilises in the most common way - the backward glider stream cuts through the debris and thenceforth extends unobstructed. I agree these patterns are not Methusalehs, but I must admit I've never thought that a well-defined or particularly interesting class.
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Re: Largest and oldest methuselah ever found!

Postby TDiff? » January 17th, 2018, 11:03 am

NickGotts wrote:I should do something about that old blog! For one thing, I didn't quite understand what a blog is supposed to be, so it's really just a website on which I've plonked various patterns. Maybe I should repost them on ConwayLife. TDiff's pattern is interesting in that the backward stream of gliders runs between the two switch engines, but otherwise much like many of the ones I found, and eventually stabilises in the most common way - the backward glider stream cuts through the debris and thenceforth extends unobstructed. I agree these patterns are not Methusalehs, but I must admit I've never thought that a well-defined or particularly interesting class.


I played along with your pattern that goes to 8 million and i found a couple of others variations :
One that will stop after 2.7 millions gen completely breaking the 2 engines running in opposite directions,
and another one that goes up to 127 millions then get stuck into a loop and keep growing until infinity

The one that breaks itself at 2.7 millions :
x = 52, y = 56, rule = B3/S23
9b4o$13bo$13bo$14b2o6$o$o$o$o$b2o$3bo$3bo25$48bo$48bo$49b2o$51bo$51bo$
51bo$51bo6$36b2o$38bo$38bo$39b4o!


The 127M pattern :
x = 52, y = 57, rule = B3/S23
9b4o$13bo$13bo$14b2o6$o$o$o$o$b2o$3bo$3bo26$48bo$48bo$49b2o$51bo$51bo$
51bo$51bo6$36b2o$38bo$38bo$39b4o!


So right now i'm searching symetric ones that would eventually break completely after a very large amount of generations
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Re: Largest and oldest methuselah ever found!

Postby 2718281828 » January 17th, 2018, 1:25 pm

If we allow infinite growth pattern as methuselah and just restrict ourself to the 20x20 box, then we might engineer a methuselah which uses this ark idea.
I don't have very nice examples - but I mean something like this (just with higher lifespan):
x = 20, y = 20, rule = B3/S23
18b2o$17b2o$19bo3$17b2o$16b3o$17b2o$19bo$19bo$19bo2$3o$o2bo$o$o$bo4bo$
5b3o$5b3o$8b3o!

or
x = 20, y = 20, rule = B3/S23
3b3o$2bo3bo$2b2ob2o$3bobo$3obobo2b3o$5bo3b3o5b2o$2o7bo2bo3b3o$9bo7b2o$
10bo8bo$9bobo7bo$19bo2$3o$o2bo$o$o$bo4bo$5b3o$5b3o$8b3o!


EDIT1:
x = 20, y = 20, rule = B3/S23
bob2ob2o$o2bob2o$2bo$2obo$o3b2o$bo2bo12b2o$2o14b3o$o16b2o$19bo$19bo$
19bo6$6bo$5b3o$5b3o$8b3o!

something like this 20x20 bounding box and takes more than 100k generation (exactly 112173 generations) until it stabilises. And there are likely more that last much longer.

EDIT2:
The same in a 20x20 box with 'only 37' cells (instead of 41) and 3 ticks longer lifespan:
x = 20, y = 20, rule = B3/S23
bob2ob2o$o2bob2o$2bo$2obo$o3b2o10bo$bo2bo11bo$2o15b2o$o18bo$19bo$19bo$
19bo6$4b2o$6bo$6bo$7b4o!
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Re: Largest and oldest methuselah ever found!

Postby towerator » January 17th, 2018, 6:01 pm

I think this pattern is more accurately put in the "ark" family. Indeed, its unstability comes from the fact it comes from a pair of engines that shoot backward. I don't know what's the consensus, but I don't think it's a true methusaleh a la "Iwona", "Bunnies" or the pentomino.
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Re: Largest and oldest methuselah ever found!

Postby TDiff? » January 17th, 2018, 6:31 pm

2718281828 wrote:If we allow infinite growth pattern as methuselah and just restrict ourself to the 20x20 box, then we might engineer a methuselah which uses this ark idea.
I don't have very nice examples - but I mean something like this (just with higher lifespan):
x = 20, y = 20, rule = B3/S23
18b2o$17b2o$19bo3$17b2o$16b3o$17b2o$19bo$19bo$19bo2$3o$o2bo$o$o$bo4bo$
5b3o$5b3o$8b3o!

or
x = 20, y = 20, rule = B3/S23
3b3o$2bo3bo$2b2ob2o$3bobo$3obobo2b3o$5bo3b3o5b2o$2o7bo2bo3b3o$9bo7b2o$
10bo8bo$9bobo7bo$19bo2$3o$o2bo$o$o$bo4bo$5b3o$5b3o$8b3o!


EDIT1:
x = 20, y = 20, rule = B3/S23
bob2ob2o$o2bob2o$2bo$2obo$o3b2o$bo2bo12b2o$2o14b3o$o16b2o$19bo$19bo$
19bo6$6bo$5b3o$5b3o$8b3o!

something like this 20x20 bounding box and takes more than 100k generation (exactly 112173 generations) until it stabilises. And there are likely more that last much longer.

EDIT2:
The same in a 20x20 box with 'only 37' cells (instead of 41) and 3 ticks longer lifespan:
x = 20, y = 20, rule = B3/S23
bob2ob2o$o2bob2o$2bo$2obo$o3b2o10bo$bo2bo11bo$2o15b2o$o18bo$19bo$19bo$
19bo6$4b2o$6bo$6bo$7b4o!


Hey nice!

This one is 20 x 20 , 45 for initial population, and it goes up to 140000~ before stabilizing :
x = 20, y = 20, rule = B3/S23
3o7bo2bo$obo6bo$4o5bo3bo$2b2o5b4o$16bo$16bo$17b2o$19bo$19bo$b3o15bo$o
2bo15bo$3bo$3bo$obo3$4b2o$6bo$6bo$7b4o!


A variant that does the same thing with 5 less initial cells :
x = 20, y = 20, rule = B3/S23
2obo6bo2bo$2o7bo$9bo3bo$o8b4o$16bo$16bo$17b2o$19bo$19bo$b3o15bo$o2bo
15bo$3bo$3bo$obo3$4b2o$6bo$6bo$7b4o!
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Re: Largest and oldest methuselah ever found!

Postby gameoflifeboy » January 17th, 2018, 11:59 pm

In May 2009, I found a methuselah using a single ark that takes almost as long to stabilize as ark2:

x = 55, y = 44, rule = B3/S23
48b7o28$12bo$12bo$13b2o$15bo$15bo$15bo$15bo6$2o$2bo$2bo$3b4o!


I already posted it in my online collection of useless patterns.

I guess it can be made smaller:

x = 55, y = 44, rule = B3/S23
50b2o$49bob2o$50bo26$12bo$12bo$13b2o$15bo$15bo$15bo$15bo6$2o$2bo$2bo$
3b4o!


It is 3 cells bigger than ark2 though. I wonder how many other combinations of this size last so long.

I was sure that I saw a temporary long long long snake, or longer, in the ash once, but I was never able to find it again.

EDIT: This lasts only 6228559 generations. Why did I think it lasted longer than ark2?
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Re: Largest and oldest methuselah ever found!

Postby 2718281828 » January 18th, 2018, 6:01 am

TDiff? wrote:This one is 20 x 20 , 45 for initial population, and it goes up to 140000~ before stabilizing :
x = 20, y = 20, rule = B3/S23
3o7bo2bo$obo6bo$4o5bo3bo$2b2o5b4o$16bo$16bo$17b2o$19bo$19bo$b3o15bo$o
2bo15bo$3bo$3bo$obo3$4b2o$6bo$6bo$7b4o!


A variant that does the same thing with 5 less initial cells :
x = 20, y = 20, rule = B3/S23
2obo6bo2bo$2o7bo$9bo3bo$o8b4o$16bo$16bo$17b2o$19bo$19bo$b3o15bo$o2bo
15bo$3bo$3bo$obo3$4b2o$6bo$6bo$7b4o!

awesome.

And three cells can be additionally removed, so 37 cells in a 20x20 box (which makes it even more looking like a methuselah):
x = 20, y = 20, rule = B3/S23
bobo$2o6b4o$8bo3bo$o7bo$9bo6bo$4bo11bo$3bo13b2o$2bo16bo$bo17bo$bo17bo$
bo17bo$bo$3bo4$4b2o$6bo$6bo$7b4o!

Maybe the two-bipond predecessor can be created in a cheaper way (esp when looking at at generation 10).

However, as already mentioned due to the infinite growth these no standard methuselah and they should be posted there: viewtopic.php?f=2&t=1198.
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Re: Largest and oldest methuselah ever found!

Postby 77topaz » January 20th, 2018, 5:19 am

By rights, the 20x20 ones could be listed on the LifeWiki list, since most of the other top entries are also designed to fit in a 20x20 box, and the page doesn't specify that engineered patterns as opposed to random soups don't count. Alternatively, two separate lists could be made: one for the longest-lived random patterns within a certain bounding box, and one for the longest-lived engineered (e.g. ark-based) patterns within a certain bounding box.
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Re: Largest and oldest methuselah ever found!

Postby Apple Bottom » January 20th, 2018, 5:43 am

77topaz wrote:Alternatively, two separate lists could be made: one for the longest-lived random patterns within a certain bounding box, and one for the longest-lived engineered (e.g. ark-based) patterns within a certain bounding box.


That sounds sensible to me -- though I'm actually on the fence these days whether a 20 by 20 soup with almost 200 live cells that takes 30k generations to settle down is really in the same category of pattern as a 5 by 8 pattern with 12 live cells that takes 23k to do the same. I don't think e.g. Fred and 23334M are really in the same category.

Would this be a reasonable stab at clarifying the concept of a methuselah? Although an exact definition'd remain elusive, we could broadly break down methuselahs into three types:

  • Small bounding box;
  • Large bounding box, sparse; and
  • Large bounding box, dense.

With the cut-off between "small" and "large" bounding boxes being around.. 10ish? in either direction (or otherwise so that 20x20 would be "large" but 6x4 would be "small").

(FWIW, I don't think there's much sense in separating "small bounding box" methuselah into sparse and dense; a 6x4 methuselah is always going to be "dense".)

This would give sort the current list entries as follows:

Small:

  • 23334M
  • Blom
  • Bunnies 11
  • Bunnies 10
  • Bunnies 9
  • Bunnies
  • Rabbits
  • 7468M
  • Acorn
  • Multum in parvo
  • Switch engine
  • R-pentomino relatives
  • R-pentomino grandparents
  • R-pentomino

Large, sparse:

  • 40514M
  • 35161M (or is that dense?)
  • Edna (26-cell form)
  • Eve (or is that dense as well?)
  • Lidka (or is that small?)
  • Iwona
  • Justyna

Large, dense:

  • Fred
  • 35201M
  • Edna (149-cell form)
  • Ed

As you can see, there's some doubt left just what is dense vs. sparse, or large vs. small, but most patterns are fairly clearly in one category.

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Re: Largest and oldest methuselah ever found!

Postby Macbi » January 20th, 2018, 6:42 am

I'm probably repeating what I've said elsewhere, but I've always thought that "minimum covering polyplet" is the best notion of size because it penalizes both population and bounding box. So it would be a principled way of judging methusalae on just one number. I'm on my phone right now so I can't calculate it for all of them but I'll give it a go later.
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Re: Largest and oldest methuselah ever found!

Postby Apple Bottom » January 20th, 2018, 8:14 am

Macbi wrote:I'm probably repeating what I've said elsewhere, but I've always thought that "minimum covering polyplet" is the best notion of size because it penalizes both population and bounding box. So it would be a principled way of judging methusalae on just one number. I'm on my phone right now so I can't calculate it for all of them but I'll give it a go later.


This sounds intriguing. Can you explain what this means, and how it's calculated?
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Re: Largest and oldest methuselah ever found!

Postby Macbi » January 20th, 2018, 9:12 am

A polyplet is any collection of cells that is connected (diagonal connections are allowed, otherwise we would say "polyomino"). A polyplet covers a bunch of cells if it contains each of them. So I'm saying that we should judge the size of a pattern by the size of the smallest polyplet needed to cover it. Lets write mcps instead of minimal covering polyplet size. Then patterns with a large population also have a large mcps, because every cell of the population has to be in the covering polyplet. And any pattern with a large bounding box has to have a large mcps, because the polyplet has to stretch between each part of the pattern.

So although Fred has a relatively small (20 x 20) bounding box, its mcps is quite large (163) because it has a large population. And although 40514M has a relatively small population (18) its mcps is quite large (104) because it has a large bounding box.

To calculate the mcps you have to find a covering polyplet and prove that there isn't a smaller one. This sounds tricky put in practice it's easy to do. Technically finding the mcps is an instance of the Steiner tree problem and can therefore must be hard for some patterns. But I had no difficulty finding it for all the methusalahs on the list, and I'm sure a script could be written to do it even faster.
Last edited by Macbi on June 20th, 2018, 4:27 am, edited 1 time in total.
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Re: Largest and oldest methuselah ever found!

Postby Macbi » January 20th, 2018, 9:48 am

Here's the data and a rubbish graph with no labels.

Name                        x    y    Area   Pop   mcps   Lifespan
----                        -    -    ----   ---   ----   --------
40514M                      78   54   4212   18    104    40514
Fred                        20   20   400    150   163    35426
35201M                      20   20   400    183   188    35201
35161M                      32   28   896    30    66     35161
Edna (spread out version)   43   26   1118   26    73     31082
Edna (box version)          20   20   400    149   157    31192
Ed                          20   20   400    151   163    30872
Eve                         16   10   160    20    26     30046
Lidka                       15   9    135    13    21     29055
Iwona                       21   20   420    19    42     28786
Justyna                     22   17   374    20    40     26458
23334M                      8    5    40     12    14     23334
Blom                        12   5    60     13    17     23314
Bunnies 11                  6    4    24     11    12     17465
Bunnies 10                  6    6    36     10    12     17423
Bunnies 9                   8    7    56     9     12     17410
Bunnies                     8    4    32     9     11     17332
Rabbits                     7    3    21     9     10     17331
7468M                       6    4    24     8     9      7468
Acorn                       7    3    21     7     8      5206
Multum in parvo             6    4    24     7     7      3933
Switch engine               6    4    24     8     10     3911
R-pentomino relatives       6    3    18     6     7      1108
R-pentomino grandparents    4    3    12     5     5      1105
R-pentomino                 3    3    9      5     5      1103


graph.png
graph.png (10.46 KiB) Viewed 4541 times


The ones you call "Small" are precisely the ones with a mcps less than 20.
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Re: Largest and oldest methuselah ever found!

Postby simeks » January 20th, 2018, 4:04 pm

Macbi wrote:I'm probably repeating what I've said elsewhere, but I've always thought that "minimum covering polyplet" is the best notion of size because it penalizes both population and bounding box. So it would be a principled way of judging methusalae on just one number. I'm on my phone right now so I can't calculate it for all of them but I'll give it a go later.

Isn't this very similar to calculating the cost of the Minimum spanning tree, taking each on-cell as a vertice and the geometric distance between vertices as the edge cost? A mininum spanning tree is easy to find.

Apple Bottom wrote:Large, sparse:
  • ...
  • Lidka (or is that small?)
  • ...

Note that Lidka has a known smaller predecessor now.
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Re: Largest and oldest methuselah ever found!

Postby Macbi » January 20th, 2018, 4:31 pm

simeks wrote:Isn't this very similar to calculating the cost of the Minimum spanning tree, taking each on-cell as a vertice and the geometric distance between vertices as the edge cost? A mininum spanning tree is easy to find.

Similar, but the polyplet is allowed to have nodes away from the ones we want to cover. For example we could cover three nodes by a Y-shaped polyplet whose middle cell isn't itself one of the ones we want to cover.
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Re: Largest and oldest methuselah ever found!

Postby TDiff? » January 20th, 2018, 9:50 pm

I got something interesting!!

Look at this beautifull mandala :
x = 72, y = 72, rule = B3/S23
9b4o46b4o$13bo44bo$13bo44bo$14b2o40b2o6$o70bo$o70bo$o70bo$o70bo$b2o66b
2o$3bo64bo$3bo64bo41$3bo64bo$3bo64bo$b2o66b2o$o70bo$o70bo$o70bo$o70bo
6$14b2o40b2o$13bo44bo$13bo44bo$9b4o46b4o!


Also found a smaller one, very different visuals :
x = 64, y = 64, rule = B3/S23
9b4o38b4o$13bo36bo$13bo36bo$14b2o32b2o6$o62bo$o62bo$o62bo$o62bo$b2o58b
2o$3bo56bo$3bo56bo33$3bo56bo$3bo56bo$b2o58b2o$o62bo$o62bo$o62bo$o62bo
6$14b2o32b2o$13bo36bo$13bo36bo$9b4o38b4o!


Aaaand another one, also smaller :
x = 56, y = 56, rule = B3/S23
9b4o30b4o$13bo28bo$13bo28bo$14b2o24b2o6$o54bo$o54bo$o54bo$o54bo$b2o50b
2o$3bo48bo$3bo48bo25$3bo48bo$3bo48bo$b2o50b2o$o54bo$o54bo$o54bo$o54bo
6$14b2o24b2o$13bo28bo$13bo28bo$9b4o30b4o!


Another one lol :
x = 49, y = 49, rule = B3/S23
9b4o23b4o$13bo21bo$13bo21bo$14b2o17b2o6$o47bo$o47bo$o47bo$o47bo$b2o43b
2o$3bo41bo$3bo41bo18$3bo41bo$3bo41bo$b2o43b2o$o47bo$o47bo$o47bo$o47bo
6$14b2o17b2o$13bo21bo$13bo21bo$9b4o23b4o!


WOW, there is a 40 x 40 mandala! Amazing! :
x = 40, y = 40, rule = B3/S23
9b4o14b4o$13bo12bo$13bo12bo$14b2o8b2o6$o38bo$o38bo$o38bo$o38bo$b2o34b
2o$3bo32bo$3bo32bo9$3bo32bo$3bo32bo$b2o34b2o$o38bo$o38bo$o38bo$o38bo6$
14b2o8b2o$13bo12bo$13bo12bo$9b4o14b4o!
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Re: Largest and oldest methuselah ever found!

Postby Apple Bottom » January 21st, 2018, 8:56 am

Macbi wrote:Here's the data and a rubbish graph with no labels.

[...]

The ones you call "Small" are precisely the ones with a mcps less than 20.


Cool, thanks. I've updated the on-wiki list with information on each entry's MCPS and L/MCPS. Using the latter measure, simeks's Lidka predecessor, Rabbits, 23334M and the various Bunnies are the "best" methuselahs listed, followed by Lidka, Blom and Eve. 40514M is relegated to the bottom third.

I'm not sure if L/MCPS is the best measure, of course. On average, across all patterns that eventually settle down (i.e. do not exhibit infinite or "weird" growth, or stay aperiodic forever), how does lifespan relate to initial population? I'm sure L is proportional to P^α for some α; are there any estimates for α? If so, I feel L/MCPS^α would be a better measure of the "quality" of a methuselah.
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Re: Largest and oldest methuselah ever found!

Postby 77topaz » January 21st, 2018, 8:23 pm

Apple Bottom wrote:Cool, thanks. I've updated the on-wiki list with information on each entry's MCPS and L/MCPS. Using the latter measure, simeks's Lidka predecessor, Rabbits, 23334M and the various Bunnies are the "best" methuselahs listed, followed by Lidka, Blom and Eve. 40514M is relegated to the bottom third.

I'm not sure if L/MCPS is the best measure, of course. On average, across all patterns that eventually settle down (i.e. do not exhibit infinite or "weird" growth, or stay aperiodic forever), how does lifespan relate to initial population? I'm sure L is proportional to P^α for some α; are there any estimates for α? If so, I feel L/MCPS^α would be a better measure of the "quality" of a methuselah.


Good work! :D Though, I think it would also be nice to have a list of the ark-based methuselahs as well.
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Re: Largest and oldest methuselah ever found!

Postby NickGotts » January 22nd, 2018, 7:38 am

I think it would also be nice to have a list of the ark-based methuselahs as well. - 77topaz


Basically, any ark that produces a backward glider stream can be combined with a small object to the rear to produce one. Exactly what object, and where, will change the outcome, and some of them (there seems no way of predicting which) will last tens of millions of steps before they stabilise.

Here are the two 16-cell arks I know of that produce a backward stream:

x = 35, y = 23, rule = S23/B3
31bo$31boo$31bobbo$$32bobo$33bo13$o3bo$bobo$bbobbo$5bo$5bo!

x = 32, y = 29, rule = S23/B3
28bo$28boo$28bobbo$$29bobo$30bo19$o3bo$bobo$bbobbo$5bo$5bo!

As they are, each lasts a few hundred thousand steps before stabilising, with the backward stream cutting through the tail debris. Adding a blonk so this stream hits it, and doesn't immediately cut through, can produce patterns lasting considerably longer before stabilising, but there would be little point in listing them all. You can see some of them at the link to my old website given earlier.
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