## Long-lived methuselahs

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### Re: Long-lived methuselahs

testitemqlstudop wrote:2->2->3->6 * 4

How many digits does that number have? Just so I can wrap my head around it a bit.
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### Re: Long-lived methuselahs

Can you put that in knuth arrows?
For reference, the way Wikipedia puts it, p→q→r = p↑ʳq and p→q = p^q
So I imagine (2->(2->3->6))*4 is (2^(2^^^^^^3))*4. = 4*2^(2^^^^^(2^^^^^2)) = 4*2^(2^^^^^4)
danny wrote:How many digits does that number have?

If I’m understanding Conway chained arrow notation correctly, ~log(4*2^(2^^^^^(2^^^^^2)), (no, I’m not calculating pLifespan. That’s a tilde) so I bet that that is still a large number (i.e. How many digits does that number have)
Though in the way it was provided, I would evaluate to 4*4, so 2 digits is your answer.
EDIT: the number of digits in a number x (base n) is (log base n of x) + 1, rounded down.
EDIT2: based on the more accurate lifespan estimate, >digits(2^^9)
Last edited by Moosey on February 1st, 2019, 8:37 pm, edited 8 times in total.
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### Re: Long-lived methuselahs

Whoops, guess I used chained-arrow notation wrong.

Anyways, it takes
on the order of 2^^^^^^^(2^^^^^^(2^^^^^(2^^^^(2^^^(2^^(2^n))))))

to get the glider to the spacefiller, which is only 1/4 of the total evolution time. Then, the tear in the agar propogates through the spacefiller, and after 4x as much time, it destroys the three corners. Now it would probably take much more time to have the triangle completely stabilize, and if it spawns a natural replicator,

testitemqlstudop

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### Re: Long-lived methuselahs

testitemqlstudop wrote:Whoops, guess I used chained-arrow notation wrong.

Anyways, it takes
on the order of 2^^^^^^^(2^^^^^^(2^^^^^(2^^^^(2^^^(2^^(2^n))))))

to get the glider to the spacefiller, which is only 1/4 of the total evolution time. Then, the tear in the agar propogates through the spacefiller, and after 4x as much time, it destroys the three corners. Now it would probably take much more time to have the triangle completely stabilize, and if it spawns a natural replicator,

I really don’t know that well about Conway chained arrow notation, so you’re probably right.
It would probably become periodic, but maybe it wouldn’t. I hope it releases a couple sir robins, possibly with new Tagalongs.
Actually, 2->2->(doesn’t matter) =4, and that thing doesn’t stabilize in 4 generations, so you used Conway chained arrow notation wrong.
But regardless, that probably lasts on the order of 2^(2^(2^(2^(2^(2^(2^n)))))) (your estimate, likely more accurate, but those arrows are misleading. It's just 2^2^2^2^2^2^2^2... because those are chained log growths. Apologies If i'm wrong) or (2^(2^^^^^4))*4 (my estimate, based on your Conway chained arrows and a generous helping of assumed parentheses), and that is bigger than
`13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096`
(From Wikipedia, 4->3->2). That number was only 4^256, while our numbers are 2^(Almost infinitely larger than 512)
EDIT:
The important question is whether that pattern is a methuselah in the classical sense.
It has an enormous MCPS.
It was engineered.
Anyone who can recognize log(log(log(log(log...)))))) growth can tell it's got a long life.
However, Its lifespan is enormous, So we should call it a methuselah anyways.
According to the forum rules, Methuselahs larger than 20*20 in bounding box are uninteresting. However, in the case of a pattern with lifespan on the order of 2^(2^^^^^4)) it might be okay to make an exception.
EDIT:
As Dani says below, This kind of pattern could be referred to as an engineered methuselah. I guess they could be notable if they last a VERY VERY VERY long time, or if they have an unusual mechanism.
This variety runs on a mechanism that delays self destruction for a long long time.
Last edited by Moosey on February 1st, 2019, 8:44 pm, edited 3 times in total.
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### Re: Long-lived methuselahs

I would use the term 'engineered methuselah' to refer to things like that. Kind of like engineered vs natural spaceships. Once loafer or one of the c/4s becomes natural we can call it natural...
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### Re: Long-lived methuselahs

danny wrote:I would use the term 'engineered methuselah' to refer to things like that. Kind of like engineered vs natural spaceships. Once loafer or one of the c/4s becomes natural we can call it natural...

Yeah, I was thinking along those lines.
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### Re: Long-lived methuselahs

By removing all but one of the delay structures, I managed to, after something like 10^20 generations, see a glider hitting the spacefiller. The spreading chaos showed an interesting periodic rake-like structure propagating along the edge between vacuum and the agar, periodically sending out gliders. However, trying to copy a selection large enough to show this (it was about 10000x10000, which is large but microscopic compared to the whole pattern at that point) caused Golly to freeze entirely.

77topaz

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### Re: Long-lived methuselahs

77topaz wrote:By removing all but one of the delay structures, I managed to, after something like 10^20 generations, see a glider hitting the spacefiller. The spreading chaos showed an interesting periodic rake-like structure propagating along the edge between vacuum and the agar, periodically sending out gliders. However, trying to copy a selection large enough to show this (it was about 10000x10000, which is large but microscopic compared to the whole pattern at that point) caused Golly to freeze entirely.

So it likely becomes periodic?
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### Re: Long-lived methuselahs

The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.

77topaz

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### Re: Long-lived methuselahs

77topaz wrote:The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.

I’ve seen something like that rake-crawler happen on (smaller) spacefillers.
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### Re: Long-lived methuselahs

Hm. It doesn't seem like just colliding a glider with the orthogonal edge of Halfmax is necessarily sufficient to get such a structure to appear:
`x = 181, y = 670, rule = B3/S23bo\$2bo\$3o588\$147b2ob2o\$146bobobobo\$146bobobobo\$144b2obo2bob2o\$143bobo4bo\$142bo3bobobob2o\$142b3obobobo2bo\$145bo2bo2b2o\$142b2o\$141bo2b3o3b3o\$141bobo9bobo\$142bobob2ob2obob2o\$144bob2ob2obo\$144bobo3bobo\$145bo5bo2\$143b11o\$143bo2bobobo2bo2\$140b2o6bo6b2o\$140bobo3b5o3bobo\$138bobob3o7b3obobo\$137bobobobo9bobobobo\$137bobobobob2o3b2obobobobo\$138bo3bob2obobob2obo3bo\$146b2ob2o\$126b2o8bo10bobo10bo8b2o\$125b2o3bo4b2o7b4ob4o7b2o4bo3b2o\$124b2o2b2o4bo3b3o3bo7bo3b3o3bo4b2o2b2o\$125bo4b5obo4bo3b3ob3o3bo4bob5o4bo\$129bo4bobo23bobo4bo\$126b2o3b2ob2obo7b3ob3o7bob2ob2o3b2o\$129b2o4bo25bo4b2o\$119b5o3b2o5bo6b2o2b2o3b2o2b2o6bo5b2o3b5o\$119bo4b2obo2bo10b2o2b3ob3o2b2o10bo2bob2o4bo\$119bo6bo18bobobobo18bo6bo\$120bo5b2obo17bobo17bob2o5bo\$122b2o2bo3b2o11b4obob4o11b2o3bo2b2o\$125bo17b2o3bo3b2o17bo\$123b3o20b2ob2o20b3o\$122bo8bo5bo5b3obobob3o5bo5bo8bo\$122bo4bobo2b2o4b2o7bobo7b2o4b2o2bobo4bo\$122bo3b2o2bob2ob2ob2ob5obobob5ob2ob2ob2obo2b2o3bo\$123bo21bobobobo21bo\$124b21o3bo3b21o2\$126b21o3b21o\$125bo21bobo21bo\$124bo3b20ob20o3bo\$121bobo2bo2bo37bo2bo2bobo\$120bo2bobo4b37o4bobo2bo\$119b2o10bo33bo10b2o\$118bo13b33o13bo\$117b4o12bo29bo12b4o\$116bo4bo12b29o12bo4bo\$116bo2bo15bo25bo15bo2bo\$116bo2bo16b25o16bo2bo\$117bo19bo21bo19bo\$118b4obo14b21o14bob4o\$119bo3bo15bo17bo15bo3bo\$120bo19b17o19bo\$120bobo18bo13bo18bobo\$142b13o\$119b3o21bo9bo21b3o\$119b2o23b9o23b2o\$119b3o26bo26b3o\$145b3ob3o\$120bobo23bo3bo23bobo\$120bo24bobobobo24bo\$119bo3bo21bobobobo21bo3bo\$118b4obo20bo7bo20bob4o\$117bo26bo7bo26bo\$116bo2bo24bo2bobo2bo24bo2bo\$116bo2bo24b3o3b3o24bo2bo\$116bo4bo53bo4bo\$117b4o55b4o\$118bo59bo\$119b2o55b2o\$120bo2bo49bo2bo\$121bobo49bobo!`

It's likely that a different, specific phase alignment between the incoming glider and the wick that stabilises the orthogonal edge is required.

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### Re: Long-lived methuselahs

77topaz wrote:The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.

I'm not sure, but it actually propgates at 2c/3 vertically and c horizontally.

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### Re: Long-lived methuselahs

testitemqlstudop wrote:
77topaz wrote:The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.

I'm not sure, but it actually propgates at 2c/3 vertically and c horizontally.

Huh. Weird nonuniform speeds. But this makes sense, because with the grain negative spaceships go at c and against the grain negative spaceships travel at 2c/3
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### Re: Long-lived methuselahs

Moosey wrote:Huh. Weird nonuniform speeds. But this makes sense, because with the grain negative spaceships go at c and against the grain negative spaceships travel at 2c/3
I think it's the other way around. Those are the speeds people searched for ships because they observed that those were the speeds at which the agar collapsed.

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### Re: Long-lived methuselahs

Macbi wrote:
Moosey wrote:Huh. Weird nonuniform speeds. But this makes sense, because with the grain negative spaceships go at c and against the grain negative spaceships travel at 2c/3
I think it's the other way around. Those are the speeds people searched for ships because they observed that those were the speeds at which the agar collapsed.

Oh, that makes sense. But still, I guess you could argue that it makes sense because the negative spaceships go at those speeds because the agar decays at those speeds.
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### Re: Long-lived methuselahs

21655 gen methuselah with nearly record-breaking F/I - rank #2, after simek's 24827M.
Pi + dove (is it a dove) + LOM predecessor = huge explosion, F/I is 274
`x = 21, y = 14, rule = B3/S2313b2o\$13bo2bo\$14bobo\$14b3o\$b2o\$2o\$bo\$2bo2\$20bo2\$16b5o\$17b3o\$18bo!`

Found with hacked apgsearch that does 10x10 soups and also catagolues f/i.

Census: b3s23/10x10

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### Re: Long-lived methuselahs

Here's a 10-cell methuselah lasting 17,425 steps - thus beating bunnies10 by just 2 steps:
`x = 6, y = 6, rule = B3/S23bo\$2obo\$4b2o\$o2bo\$o\$o!`

Step 30 of the pattern is almost the same as step 28 of bunnies10, but lacks a glider which the latter has just thrown off. It thus ends with a population of 1,744, including 40 gliders, as opposed to bunnies10's 1749 and 41 gliders. Since it's hardly a radical improvement, I suggest calling it bunnies10a. Its MCPS is 12, its bounding box 8*5.

A bit of background is available in the "Systematic survey of small patterns" thread.
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### Re: Long-lived methuselahs

NickGotts wrote:Here's a 10-cell methuselah lasting 17,425 steps - thus beating bunnies10 by just 2 steps:
`x = 6, y = 6, rule = B3/S23bo\$2obo\$4b2o\$o2bo\$o\$o!`

Step 30 of the pattern is almost the same as step 28 of bunnies10, but lacks a glider which the latter has just thrown off. It thus ends with a population of 1,744, including 40 gliders, as opposed to bunnies10's 1749 and 41 gliders. Since it's hardly a radical improvement, I suggest calling it bunnies10a. Its MCPS is 12, its bounding box 8*5.

A bit of background is available in the "Systematic survey of small patterns" thread.

I think you must have miscounted its lifespan— that IS bunnies 10
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### Re: Long-lived methuselahs

Apologies, and thanks for pointing out the error - which was not a miscount, but a miscopy, posting bunnies10 rather than the true bunnies10a, which is:
`x = 8, y = 5, rule = B3/S232bo\$ob2obo\$6bo\$o4b2o\$7bo!`
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### Re: Long-lived methuselahs

NickGotts wrote:Apologies, and thanks for pointing out the error - which was not a miscount, but a miscopy, posting bunnies10 rather than the true bunnies10a, which is:
`x = 8, y = 5, rule = B3/S232bo\$ob2obo\$6bo\$o4b2o\$7bo!`

Oh! That’s neat, and now we need to make edits to the wiki.

EDIT:
Edits made— now I need to have references properly made, as I have no Idea how to do it properly.
Since it’s closely related to bunnies 10, perhaps we should add an image and RLE to the wiki too.
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### Re: Long-lived methuselahs

A for Awesome wrote (on the Systematic survey of small patterns thread:
Trivial variant with a smaller bounding box:
Code: Select all / Show in Viewer
x = 7, y = 5, rule = B3/S23
bo\$3obo\$5bo\$o3b2o\$6bo!

With its smaller bounding box, this is clearly the preferred variant, and I suggest putting it in the wiki, and transferring the name bunnies10a to it, if A for Awesome agrees.

However, given that it had already been generated by my search, but I failed to notice it i.e. to check exactly how long it lasted (I just thought: "Ho-hum, another one of those"), it might be best to hold the wiki edit while I check the other similar patterns which have already been generated, which I can do tomorrow, just in case there's another pattern that lasts as long or even longer.
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### Re: Long-lived methuselahs

OK, I can confirm that the two 10-cell patterns already reported are the only 17425-step methuselahs to turn up so far.
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