## Smallest long-lived methuselahs

For discussion of other cellular automata.
2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Smallest long-lived methuselahs

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!``````
Last edited by 2718281828 on August 10th, 2019, 2:23 am, edited 16 times in total.

Redstoneboi
Posts: 356
Joined: May 14th, 2018, 3:57 am

### Re: Smallest long-lived methuselahs

that...
escalated quickly...
c(>^w^<c)~*
This is 「Fluffy」
「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
「Fluffy」likes to watch spaceship guns in Golly.
「Fluffy」knows Natsuki best girl.

Majestas32
Posts: 524
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

### Re: Smallest long-lived methuselahs

52521

toroidalet
Posts: 1054
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

### Re: Smallest long-lived methuselahs

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.
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

jimmyChen2013
Posts: 133
Joined: December 11th, 2017, 3:28 am

### Re: Smallest long-lived methuselahs

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
Failed Replicator!

Code: Select all

``````x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo\$obo\$bobo\$2bo!
``````
(That I wish was not failed D:)

wildmyron
Posts: 1346
Joined: August 9th, 2013, 12:45 am

### Re: Smallest long-lived methuselahs

jimmyChen2013 wrote: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 9067 times
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

jimmyChen2013
Posts: 133
Joined: December 11th, 2017, 3:28 am

### Re: Smallest long-lived methuselahs

oh.
Failed Replicator!

Code: Select all

``````x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo\$obo\$bobo\$2bo!
``````
(That I wish was not failed D:)

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

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
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

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
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

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!
``````
Last edited by 2718281828 on August 8th, 2019, 3:30 pm, edited 2 times in total.

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

toroidalet wrote: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
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

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
Posts: 1476
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Smallest long-lived methuselahs

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!
``````
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

``````x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o\$6bo\$o3b3o\$2o\$bo!
``````

77topaz
Posts: 1467
Joined: January 12th, 2018, 9:19 pm

### Re: Smallest long-lived methuselahs

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

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

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).

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

New record for MCP=2:

Code: Select all

``````x = 2, y = 1, rule = B2ac3nq4aiy5aci7e8/S13kr4ceit7e
2o!
``````
L=92

toroidalet
Posts: 1054
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

### Re: Smallest long-lived methuselahs

MCPS=1, L=67:

Code: Select all

``````x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3jry4artw5y6c
o!
``````
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

Hdjensofjfnen
Posts: 1476
Joined: March 15th, 2016, 6:41 pm
Location: r cis θ

### Re: Smallest long-lived methuselahs

toroidalet wrote:MCPS=1, L=67:

Code: Select all

``````x = 1, y = 1, rule = B1e2i3k4acw5y7e8/S12-e3jry4artw5y6c
o!
``````
Wow, that's a new record!
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

``````x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o\$6bo\$o3b3o\$2o\$bo!
``````

jimmyChen2013
Posts: 133
Joined: December 11th, 2017, 3:28 am

### Re: Smallest long-lived methuselahs

toroidalet wrote: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!
``````
Failed Replicator!

Code: Select all

``````x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo\$obo\$bobo\$2bo!
``````
(That I wish was not failed D:)

2718281828
Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

toroidalet wrote: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
Posts: 133
Joined: December 11th, 2017, 3:28 am

### Re: Smallest long-lived methuselahs

Cool im blind
But this is fine

Code: Select all

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

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!
``````
Failed Replicator!

Code: Select all

``````x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8
bo\$obo\$bobo\$2bo!
``````
(That I wish was not failed D:)

melwin22
Posts: 31
Joined: September 9th, 2017, 5:40 am

### Re: Smallest long-lived methuselahs

jimmyChen2013 wrote: 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
Posts: 3056
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board. Or [click to not expand]
Contact:

### Re: Smallest long-lived methuselahs

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
Last edited by Moosey on July 24th, 2019, 10:59 am, edited 1 time in total.
I am a prolific creator of many rather pathetic googological functions

My CA rules can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"

AforAmpere
Posts: 1079
Joined: July 1st, 2016, 3:58 pm

### Re: Smallest long-lived methuselahs

Moosey wrote: 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.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

melwin22
Posts: 31
Joined: September 9th, 2017, 5:40 am

### Re: Smallest long-lived methuselahs

Moosey wrote: @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!
``````
Last edited by melwin22 on July 24th, 2019, 3:09 pm, edited 2 times in total.