Smallest long-lived methuselahs

[2718281828]

We have the a list of smallest oscillators and spaceships for certain periods and speeds. I thought about a list of long-lived methuselahs in isotropic non-totalistic Life-like cellular automaton (without B0).

I know we have no strict definition for a methuselah, therefore I think it makes sense to consider first only:
- pattern that are empty or a collection of oscillators (inc. still lifes) and spaceships after a certain period of time (to avoid all growth pattern and pathologicals)
--> the time till this is achieved is the life span L.


For measuring the size of the methuselah I suggest MCPS (minimum covering polyplet size).

Here a start:
MCPS=2, L=2:

Code: Select all

x = 2, y = 2, rule = B2e/S1c
bo$o!

MCPS=3, L=52,521:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any678
o$bo$2bo!

EDIT1: recent records (credits see below)

MCPS=1, L=128:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acjw5ny7e8/S12-e3jkry4artw5y6c
o!

MCPS=2, L=154:

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4ajw5n6e8/S12-e3jkr4artw5nr6an
o$bo!

MCPS=3, L=3,202,328,906:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5aein6ikn7/S2ce3any4acnyz5-ce6-k7e8
o$bo$2bo!

[Redstoneboi]

that...
escalated quickly...

[Majestas32]

52521

[toroidalet]

L=2 from 2 to 32:

Code: Select all

x = 2, y = 1, rule = B2-en4q6c7e/S2i3y4c
2o!

even this likely isn't the maximum, as I found this in a few minutes manually.

[jimmyChen2013]

can anyone check if this one is explosive?
my pc is too bad to run it

Code: Select all

x = 3, y = 3, rule = B3-k4ceq5cei678/S2-a34cet5cei6-c78
bo$obo$bo!

B3-k4ce5cei678/S2-a34cet5cei6-c78
this rule has some potential
the same 4 cells run for about 23000

[wildmyron]

can anyone check if this one is explosive?
my pc is too bad to run it

Code: Select all

x = 3, y = 3, rule = B3-k4ceq5cei678/S2-a34cet5cei6-c78
bo$obo$bo!

It seems very likely that this tub is explosive.

Exploding tub after 526k gen

alien_tub.png (104.44 KiB) Viewed 15117 times

[jimmyChen2013]

oh.

[2718281828]

I think for MCP=4 it is worth considering something in C1, e.g. based on this:

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr
o$o$o$bo!

I just tried some extensions manually and received this (better run it in golly)

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr6n
o$o$o$bo!

with L= 54855, so slightly better than the MCP=3 methuselah above. This is also quite lucky as there is a temporary natural linear growth which appears around generation 49k and 'dies' about 2k generations later:

Code: Select all

x = 9, y = 6, rule = B2c3aij4cez/S1c2-i34cr6n
6b2o$6b2o$6bo$7bo$3b3o$3b2obo!

EDIT1: something better:

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr5a6n
o$o$o$bo!

L= 88594
it is again a single huge thing plus this natural glider (around gen 21k):

Code: Select all

x = 27, y = 21, rule = B2c3aij4cez/S1c2-i34cr5a6n
7$11bo$9b2o$8b2obo2bo$12b2o$12bo!

EDIT2: This one should have L=162098:

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr5a6n8
o$o$o$bo!

EDIT3:
Unfortunately this exhibits linear growth around L>120k.

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez8/S1c2-i34crt5a
o$o$o$bo!

EDIT4: If this converges, it has L>1240k, but I am not sure - my computer is too slow, still I am confident that this is a methuselah. Until gen 1240k it does not show any (temporary) linear growth pattern.

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$o$o$bo!

And similarly this 4 MCP pattern (L>680k):

Code: Select all

x = 3, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$bo$bo$2bo!

[2718281828]

Okay, this is the new record for MCP=4:

Code: Select all

x = 2, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$o$o$bo!

with L>1250k (and L<1480k). Unfortunately I don't have it more precise.
Moreover, this

Code: Select all

x = 3, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$bo$bo$2bo!

has L< 825k.

[2718281828]

MCP=3 and L= 109350:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any5r678
2bo$bo$o!

much better L=1,608,343:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any5kr678
2bo$bo$o!

and L=2,278,427:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5any678/S2ce3any4any5kr678
2bo$bo$o!

EDIT1: something similar with L=14,817,124:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5any678/S2ce3any4aeny5kr67c8
2bo$bo$o!

EDIT2: L=98,975,157:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2bo$bo$o!

This one will likely work with L>217M:

Code: Select all

x = 3, y = 3, rule = B2-a3-any5-jkqr67/S2ce3any4aenyz5ikr6-en7c8
2bo$bo$o!

[2718281828]

L=2 from 2 to 32:

Code: Select all

x = 2, y = 1, rule = B2-en4q6c7e/S2i3y4c
2o!

even this likely isn't the maximum, as I found this in a few minutes manually.

Slightly better with a similar rule, L=36:

Code: Select all

x = 2, y = 1, rule = B2-en7e/S2i3ry4ci5j6c
2o!

Edit1: L=56:

Code: Select all

x = 2, y = 1, rule = B2-en5e7e8/S2i3kry4cikt5j6c
2o!

[2718281828]

MCP=3, 2 cells: L= 5257

Code: Select all

x = 3, y = 1, rule = B2c3acer4cejnz5678/S01e2-ae3-jnq4aeiqy5ajnqr6-ci7e8
obo!

Maybe something with L>1M is possible in this setting as well. At least the pattern structure looks similar to the record holder with MCP=3 (and 3 cells).

[Hdjensofjfnen]

I was surprised the previous record-holder was less than 100, see this M168:

Code: Select all

x = 3, y = 1, rule = B2c3ae4e/S01c23c
obo!

EDIT:

Code: Select all

x = 3, y = 1, rule = B2cn3aejy4ew/S01e2c3c
obo!

EDIT: A welcome bonus:

Code: Select all

x = 61, y = 22, rule = B2cn3aejy4ew/S01e2c3c5r
58bobo17$2bo$o2$o$3bo!

[77topaz]

These exponentially long-lived methuselahs by toroidalet may also be of interest for this thread.

[2718281828]

I was surprised the previous record-holder was less than 100, see this M168:

This is still the record holder for MCPS=2 (http://www.conwaylife.com/wiki/MCPS). And the pattern above has MPCS=3 (but 2 cells).

[2718281828]

New record for MCP=2:

Code: Select all

x = 2, y = 1, rule = B2ac3nq4aiy5aci7e8/S13kr4ceit7e
2o!

L=92

[toroidalet]

MCPS=1, L=67:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3jry4artw5y6c
o!

[Hdjensofjfnen]

MCPS=1, L=67:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3jry4artw5y6c
o!

Wow, that's a new record!

[jimmyChen2013]

MCPS=1, L=67:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3jry4artw5y6c
o!

If am getting the rules right, a slight modification gives MCPS=1, L=95 (someone verify)

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acqw5y7e8/S12-e3jry4artw5y6c
o!

Also, this funny little thing showed up:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3ijry4artw5y6c
o!

Does this count?

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw7e8/S12-e3jry4artw5y6c
o!

L=95-ish

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5ny7e8/S12-e3jry4artw5y6c
o!

L=110-ish

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5ny6a7e8/S12-e3jry4artw5y6c7c
o!

I hope wickstretchers count

EDIT:
Unrelated:
Infinite prison for semi-p12:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acew5y7e8/S1e2-e3jry4artw5y6c
o!

Tack gun!

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acew5y7e8/S1e2-e3ry4artw5y6c
o!

[2718281828]

MCPS=1, L=67:

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3jry4artw5y6c
o!

Great!

@ jimmyChen2013, as mentioned in the first post, no infinite growth pattern are allowed.

[jimmyChen2013]

Cool im blind
But this is fine

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acw5ny7e8/S12-e3jry4artw5y6c
o!

it adds another layer

EDIT:
and yet another: L=128

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acjw5ny7e8/S12-e3jkry4artw5y6c
o!

Unrelated Pi-rake turned up

Code: Select all

x = 4, y = 3, rule = B1e2i3k4acjw5ny7e8/S12-e3jkry4artw5y
2o$b3o$2o!

[melwin22]

it adds another layer

EDIT:
and yet another: L=128

Code: Select all

x = 1, y = 1, rule = B1e2i3k4acjw5ny7e8/S12-e3jkry4artw5y6c
o!

So this is much better than MCP=2 L=92, mentioned in first post as "record". Great work!

In outer-totallistic rules, MCP=1 will either explode to infinity or disappear immediately, so this is not fun. I think this is the best result for MCP=2 (L=12)

Code: Select all

x = 1, y = 2, rule = B2/S0
o$o!

For MCP=3, I can't found anything better than L=25

Code: Select all

x = 3, y = 3, rule = B28/S04
o$bo$2bo!

though I'm almost sure there are longer lifespans somewhere.

Other methuselahs that I discovered (idk if this is off-topic, sorry if so):

Code: Select all

x = 13, y = 6, rule = B3678/S135678
2bo2$ob2o6bo$2bo6b2obo2$10bo!

lifespan ~ 73100, MCPS = 17, grows over 200k times.

Code: Select all

x = 37, y = 9, rule = B3678/S135678
2bo2$ob2o$2bo2$34bo$33b2obo2$34bo!

lifespan ~ 92870, MCPS = 41, grows over 350k times (record for this rule so far)

[Moosey]

Various long-lived ones I found.

good catch, aforampere MCPS= 28; lifespan ~= 200B

Code: Select all

x = 21, y = 21, rule = B2a3jry4iy5y/S
19b2o$19b2o16$b2obo$o3bo$o$b2o!

MCPS = 7; Lifespan ~= 60K

Code: Select all

x = 3, y = 6, rule = B3-cqy4j/S2-n34i
2bo$bo$bo$obo$bo$bo!

@melwin22: Here's a fairly long-lived MCPS=3 methuselah in an OT rule

Code: Select all

x = 3, y = 2, rule = B38/S12345678
obo$bo!

L=2109

[AforAmpere]

MCPS= 29; lifespan ~= 200B

Code: Select all

x = 21, y = 21, rule = B2a3jry4iy5y/S
19b2o$19b2o16$b2obo$o3bo$o$b2o!

This one's great. It lasts exactly 255,622,213,276 generations. Though doesn't MCPS=28?

This one has a higher MCPS (31), but lasts 387,670,205,981:

Code: Select all

x = 21, y = 21, rule = B2a3jry4iy5y/S
19b2o$19b2o16$b2obo$o3bo$o$b2o!

EDIT, MCPS = 56 and it lasts 7,925,984,864,249,960:

Code: Select all

x = 50, y = 38, rule = B2a3jry4iy5y/S
48b2o$48b2o33$b2obo$o3bo$o$b2o!

Though I'm sure there are much better ones with that high MCPS.

[melwin22]

@melwin22: Here's a fairly long-lived MCPS=3 methuselah in an OT rule

Code: Select all

x = 3, y = 2, rule = B38/S12345678
obo$bo!

L=2109

I thought that infinite growth is not allowed.

And - guys, how do you even simulate this things for billions of generations? O.O

EDIT: non-infinite growth, L=81.

Code: Select all

x = 3, y = 2, rule = B3578/S12568
bo$obo!