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Smallest long-lived methuselahs

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Smallest long-lived methuselahs

Postby 2718281828 » May 23rd, 2018, 2:21 pm

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 MCP (minimum covering polyplet).

Here a start:
MCP=2, L=2:
x = 2, y = 2, rule = B2e/S1c
bo$o!

MCP=3, L=52,521:
x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any678
o$bo$2bo!



EDIT1: actual records (credits see below)

MCP=2, L=56:
x = 2, y = 1, rule = B2-en5e7e8/S2i3kry4cikt5j6c
2o!

MCP=3, L=98,975,157:
x = 3, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2bo$bo$o!
Last edited by 2718281828 on May 27th, 2018, 5:25 pm, edited 11 times in total.
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Re: Smallest long-lived methuselahs

Postby Redstoneboi » May 23rd, 2018, 4:17 pm

that...
escalated quickly...
c(>^w^<c)~*
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Re: Smallest long-lived methuselahs

Postby Majestas32 » May 23rd, 2018, 4:37 pm

52521
Please, stop spam searching Snowflakes.
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Re: Smallest long-lived methuselahs

Postby toroidalet » May 23rd, 2018, 5:01 pm

L=2 from 2 to 32:
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.
x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai
8b2o$2o3b2o$bo4bo3bo$2bo2b2o$o7bo!

(Check Gen 2)
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Re: Smallest long-lived methuselahs

Postby jimmyChen2013 » May 25th, 2018, 1:05 am

can anyone check if this one is explosive?
my pc is too bad to run it
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
Failed Replicator!
x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo$obo$bobo$2bo!

(That I wish was not failed D:)
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Re: Smallest long-lived methuselahs

Postby wildmyron » May 25th, 2018, 2:35 am

jimmyChen2013 wrote:can anyone check if this one is explosive?
my pc is too bad to run it
x = 3, y = 3, rule = B3-k4ceq5cei678/S2-a34cet5cei6-c78
bo$obo$bo!

It seems very likely that this tub is explosive.
alien_tub.png
Exploding tub after 526k gen
alien_tub.png (104.44 KiB) Viewed 2675 times
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Re: Smallest long-lived methuselahs

Postby jimmyChen2013 » May 25th, 2018, 3:22 am

oh.
Failed Replicator!
x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo$obo$bobo$2bo!

(That I wish was not failed D:)
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Re: Smallest long-lived methuselahs

Postby 2718281828 » May 25th, 2018, 3:44 am

I think for MCP=4 it is worth considering something in C1, e.g. based on this:
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)
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:
x = 9, y = 6, rule = B2c3aij4cez/S1c2-i34cr6n
6b2o$6b2o$6bo$7bo$3b3o$3b2obo!



EDIT1: something better:
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):
x = 27, y = 21, rule = B2c3aij4cez/S1c2-i34cr5a6n
7$11bo$9b2o$8b2obo2bo$12b2o$12bo!


EDIT2: This one should have L=162098:
x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr5a6n8
o$o$o$bo!


EDIT3:
Unfortunately this exhibits linear growth around L>120k.
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.
x = 2, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$o$o$bo!

And similarly this 4 MCP pattern (L>680k):
x = 3, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$bo$bo$2bo!
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Re: Smallest long-lived methuselahs

Postby 2718281828 » May 26th, 2018, 10:34 am

Okay, this is the new record for MCP=4:
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
x = 3, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6c
o$bo$bo$2bo!

has L< 825k.
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Re: Smallest long-lived methuselahs

Postby 2718281828 » May 26th, 2018, 3:04 pm

MCP=3 and L= 109350:
x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any5r678
2bo$bo$o!

much better L=1,608,343:
x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any5kr678
2bo$bo$o!

and L=2,278,427:
x = 3, y = 3, rule = B2-a3-any5any678/S2ce3any4any5kr678
2bo$bo$o!


EDIT1: something similar with L=14,817,124:
x = 3, y = 3, rule = B2-a3-any5any678/S2ce3any4aeny5kr67c8
2bo$bo$o!


EDIT2: L=98,975,157:
x = 3, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2bo$bo$o!


This one will likely work with L>217M (but it is still running):
x = 3, y = 3, rule = B2-a3-any5-jkqr67/S2ce3any4aenyz5ikr6-en7c8
2bo$bo$o!
Last edited by 2718281828 on May 27th, 2018, 5:24 pm, edited 1 time in total.
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Re: Smallest long-lived methuselahs

Postby 2718281828 » May 27th, 2018, 8:04 am

toroidalet wrote:L=2 from 2 to 32:
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:
x = 2, y = 1, rule = B2-en7e/S2i3ry4ci5j6c
2o!


Edit1: L=56:
x = 2, y = 1, rule = B2-en5e7e8/S2i3kry4cikt5j6c
2o!
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Re: Smallest long-lived methuselahs

Postby 2718281828 » January 18th, 2019, 11:43 am

MCP=3, 2 cells: L= 5257
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).
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Re: Smallest long-lived methuselahs

Postby Hdjensofjfnen » January 18th, 2019, 3:33 pm

I was surprised the previous record-holder was less than 100, see this M168:
x = 3, y = 1, rule = B2c3ae4e/S01c23c
obo!

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

EDIT: A welcome bonus:
x = 61, y = 22, rule = B2cn3aejy4ew/S01e2c3c5r
58bobo17$2bo$o2$o$3bo!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Smallest long-lived methuselahs

Postby 77topaz » January 18th, 2019, 5:16 pm

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

Postby 2718281828 » January 18th, 2019, 5:23 pm

Hdjensofjfnen wrote: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).
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