## Smallest long-lived methuselahs

For discussion of other cellular automata.

### 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 MCP (minimum covering polyplet).

Here a start:
MCP=2, L=2:
`x = 2, y = 2, rule = B2e/S1cbo\$o!`

MCP=3, L=52,521:
`x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any678o\$bo\$2bo!`

EDIT1: actual records (credits see below)

MCP=2, L=56:
`x = 2, y = 1, rule = B2-en5e7e8/S2i3kry4cikt5j6c2o!`

MCP=3, L=98,975,157:
`x = 3, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e82bo\$bo\$o!`
Last edited by 2718281828 on May 27th, 2018, 5:25 pm, edited 11 times in total.

2718281828

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

### Re: Smallest long-lived methuselahs

that...
escalated quickly...
c(>^w^<c)~*
This is Fluffy the cat.
Fluffy wants to discover new things that everyone likes.
Fluffy likes to watch spaceship guns in Golly.
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Redstoneboi

Posts: 332
Joined: May 14th, 2018, 3:57 am

### Re: Smallest long-lived methuselahs

52521

Majestas32

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

### Re: Smallest long-lived methuselahs

L=2 from 2 to 32:
`x = 2, y = 1, rule = B2-en4q6c7e/S2i3y4c2o!`

even this likely isn't the maximum, as I found this in a few minutes manually.
`x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai8b2o\$2o3b2o\$bo4bo3bo\$2bo2b2o\$o7bo!`

(Check Gen 2)

toroidalet

Posts: 936
Joined: August 7th, 2016, 1:48 pm
Location: my computer

### Re: Smallest long-lived methuselahs

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-c78bo\$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-jqry4cent5j67c8bo\$obo\$bobo\$2bo!`

(That I wish was not failed D:)

jimmyChen2013

Posts: 126
Joined: December 11th, 2017, 3:28 am

### Re: Smallest long-lived methuselahs

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-c78bo\$obo\$bo!`

It seems very likely that this tub is explosive.
Exploding tub after 526k gen
alien_tub.png (104.44 KiB) Viewed 2669 times
wildmyron

Posts: 1071
Joined: August 9th, 2013, 12:45 am

### Re: Smallest long-lived methuselahs

oh.
Failed Replicator!
`x = 4, y = 4, rule = B34ce5cen67c8/S2-i3-jqry4cent5j67c8bo\$obo\$bobo\$2bo!`

(That I wish was not failed D:)

jimmyChen2013

Posts: 126
Joined: December 11th, 2017, 3:28 am

### Re: Smallest long-lived methuselahs

I think for MCP=4 it is worth considering something in C1, e.g. based on this:
`x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cro\$o\$o\$bo!`

I just tried some extensions manually and received this (better run it in golly)
`x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr6no\$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-i34cr6n6b2o\$6b2o\$6bo\$7bo\$3b3o\$3b2obo!`

EDIT1: something better:
`x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr5a6no\$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-i34cr5a6n7\$11bo\$9b2o\$8b2obo2bo\$12b2o\$12bo!`

EDIT2: This one should have L=162098:
`x = 2, y = 4, rule = B2c3aij4cez/S1c2-i34cr5a6n8o\$o\$o\$bo!`

EDIT3:
Unfortunately this exhibits linear growth around L>120k.
`x = 2, y = 4, rule = B2c3aij4cez8/S1c2-i34crt5ao\$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-i34crz5a6co\$o\$o\$bo!`

And similarly this 4 MCP pattern (L>680k):
`x = 3, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6co\$bo\$bo\$2bo!`

2718281828

Posts: 648
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

Okay, this is the new record for MCP=4:
`x = 2, y = 4, rule = B2c3aij4cez5i6ik/S1c2-i34crz5a6co\$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-i34crz5a6co\$bo\$bo\$2bo!`

has L< 825k.

2718281828

Posts: 648
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

MCP=3 and L= 109350:
`x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any5r6782bo\$bo\$o!`

much better L=1,608,343:
`x = 3, y = 3, rule = B2-a3-any5any67/S2ce3any4any5kr6782bo\$bo\$o!`

and L=2,278,427:
`x = 3, y = 3, rule = B2-a3-any5any678/S2ce3any4any5kr6782bo\$bo\$o!`

EDIT1: something similar with L=14,817,124:
`x = 3, y = 3, rule = B2-a3-any5any678/S2ce3any4aeny5kr67c82bo\$bo\$o!`

EDIT2: L=98,975,157:
`x = 3, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e82bo\$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-en7c82bo\$bo\$o!`
Last edited by 2718281828 on May 27th, 2018, 5:24 pm, edited 1 time in total.

2718281828

Posts: 648
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

toroidalet wrote:L=2 from 2 to 32:
`x = 2, y = 1, rule = B2-en4q6c7e/S2i3y4c2o!`

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/S2i3ry4ci5j6c2o!`

Edit1: L=56:
`x = 2, y = 1, rule = B2-en5e7e8/S2i3kry4cikt5j6c2o!`

2718281828

Posts: 648
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

MCP=3, 2 cells: L= 5257
`x = 3, y = 1, rule = B2c3acer4cejnz5678/S01e2-ae3-jnq4aeiqy5ajnqr6-ci7e8obo!`

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).

2718281828

Posts: 648
Joined: August 8th, 2017, 5:38 pm

### Re: Smallest long-lived methuselahs

I was surprised the previous record-holder was less than 100, see this M168:
`x = 3, y = 1, rule = B2c3ae4e/S01c23cobo!`

EDIT:
`x = 3, y = 1, rule = B2cn3aejy4ew/S01e2c3cobo!`

EDIT: A welcome bonus:
`x = 61, y = 22, rule = B2cn3aejy4ew/S01e2c3c5r58bobo17\$2bo\$o2\$o\$3bo!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

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Location: r cis θ

### Re: Smallest long-lived methuselahs

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

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 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

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