Smallest long-lived methuselahs

[Moosey]

Guys, how do you even simulate this things for billions of generations? O.O

Do you have golly? You can use hashlife and turn the step up really high. Tutorials/Golly may be a helpful page if you need help with golly. So may Tutorials/More Golly.

If you don't have golly you can go to the golly download link right on this website.

[melwin22]

Yes, I have golly, but I didn't know about ather algorithms. Thanks

The uber-methuselah which has lifespan of 7*10^15 is really neat, but its population still grows to infinity, and that was supposed to be not allowed. We can open a new topic for infinite-growing patterns probably?

[Moosey]

The uber-methuselah which has lifespan of 7*10^15 is really neat, but its population still grows to infinity, and that was supposed to be not allowed. We can open a new topic for infinite-growing patterns probably?

Probably a good idea unless we allow infinite growth in this thread.
Honestly, I'm not sure why we need that rule as it's fairly easy to get an exact lifespan even with infinite growth.

[melwin22]

again about this

L=128

Code: Select all

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

I've simplified it a bit, lifespan stays the same

Code: Select all

x = 1, y = 1, rule = B1e2i3k4ajw5y8/S12-e3jkry4artw5y6c
o!

and if we allow infinite growth, this takes about 197 gens to stabilize if I'm counting correctly

Code: Select all

x = 1, y = 1, rule = B1e2i3k4ajw5y8/S12-e3jkry4artw5y6c78
o!

[Moosey]

These have large mcps, but beat MANY MANY other objects:

EDIT: here's our tetrationally long-lived methuselah which definitely stabilizes:

Code: Select all

x = 21, y = 53, rule = B2a3ijry4ity5ey/S3i4ent5er6i
10b2o$10b2o7$7b3o2b3o2$7b3o2b3o2$bo5b3o2b3o4bo$3o15b3o$bo5b3o2b3o4bo4$
7b3o2b3o2$7bobo2bobo2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o
4$7b3o2b3o2$7bobo2bobo2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o2$7b3o2b3o2$7b3o2b
3o!

I believe that the below object beats those really long-lived methuselahs toroidalet made.

Code: Select all

x = 21, y = 53, rule = B2a3ijry4ity5ey/S3i4ent5er6i
10b2o$10b2o7$7b3o2b3o2$7b3o2b3o2$7b3o2b3o$bo17bo$3o4b3o2b3o3b3o$bo17bo
3$7b3o2b3o2$7bobo2bobo2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o4$7b3o2b3o2$7b3o2b
3o4$7b3o2b3o2$7bobo2bobo2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o2$7b3o2b3o2$7b3o
2b3o!

The first object lasts at least several million gens (and probably larger than that, possibly 2^65536); thus the second lasts roughly 2^(at least a million but likely far larger) gens (EDIT: I was wrong, better patterns shown below)

You'll need to create a new scoring method to give these a somewhat small score since any extra mcps makes practically no change in the terrifying magnitude of these objects if you're taking 2 to the previous lifespan.

Unfortunately they eventually produce infinite growth, however it may be possible to fix:

Code: Select all

x = 21, y = 79, rule = B2a3ijry4ity5ey/S3i4ent5er6i
8bo4bo$7b3o2b3o$8bo4bo$7bo6bo$6b3o4b3o$5bobo6bobo$4b3o8b3o$5bo10bo19$
10b2o$10b2o7$7b3o2b3o$bo17bo$3o4b3o2b3o3b3o$bo17bo$7b3o2b3o2$7b3o2b3o
4$7b3o2b3o2$7bobo2bobo2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o4$7b3o2b3o2$7b3o2b
3o4$7b3o2b3o2$7bobo2bobo2$7b3o2b3o4$7b3o2b3o2$7b3o2b3o2$7b3o2b3o2$7b3o
2b3o!

If the large infinite growth can be turned into a spaceship then it's not even breaking the rules.


Honestly I don't understand why we need the "no infinite growth" rule

EDIT:
Perhaps this could work better

Code: Select all

x = 8, y = 15, rule = B2a3ijry4ity5ey/S3i4ent5er6i
3b2o$3b2o13$3o2b3o!

EDIT:
This lasts ~65536 gens:

Code: Select all

x = 19, y = 15, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o8$bo15bo$3o13b3o$bo15bo3$6b3o2b3o!

This lasts ~2^(65536/6) (>2^10922, thus >> googol)

Code: Select all

x = 19, y = 15, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o10$bo15bo$3o13b3o$bo15bo$6b3o2b3o!

And this, about as long as my other one (>googolplex gens):

Code: Select all

x = 19, y = 16, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o12$bo15bo$3o3b3o2b3o2b3o$bo15bo!

EDIT it pulls by 2, not 1. Fixed patterns.

[CoolCreeper39]

B2/S:

MCP 2: 5 Generations

Code: Select all

x = 0, y = 0, rule = B2/S
o$o!

MCP 3: 9 Generations

Code: Select all

x = 0, y = 0, rule = B2/S
bo$obo!

MCP 4: 12 Generations

Code: Select all

x = 0, y = 0, rule = B2/S
4o!

[CoolCreeper39]

Brian’s Brain:

MCP 2: 3 Generations

Code: Select all

x = 2, y = 2, rule = /2/3
.A$A!

MCP 3: 10 Generations

Code: Select all

x = 1, y = 3, rule = /2/3
A2$A!

MCP 4: 13 Generations

Code: Select all

x = 1, y = 4, rule = /2/3
A2$A$A!

[Moosey]

EDIT your posts please.

[CoolCreeper39]

So far, the records are:

MCPS=1, L=128, found by jimmyChen2013 on 22/6/2019:

Code: Select all

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

MCPS=2, L=155, found by 2718281828 on 7/8/2019:

Code: Select all

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

MCPS=3, L=3,202,328,906, found by 2718281828 on 8/9/2019:
x = 3, y = 3, rule = B2-a3-any5aein6ikn7/S2ce3any4acnyz5-ce6-k7e8
o$bo$2bo!

MCPS=4, L=3,202,328,906, found by CoolCreeper39 on 8/10/2019:

Code: Select all

x = 4, y = 3, rule = B2-a3-any5aein6ikn7/S2ce3any4acnyz5-ce6-k7e8
2o$2bo$3bo!

MCPS=5, L=3,202,328,909, found by CoolCreeper39 on 8/10/2019:

Code: Select all

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

MCPS=6, L=3,202,328,908, found by CoolCreeper39 on 8/10/2019:

Code: Select all

x = 3, y = 4, rule = B2-a3-any5aein6ikn7/S2ce3any4acnyz5-ce6-k7e8
bo$2bo$bo$obo!

[Moosey]

Better mcps=4:

Code: Select all

x = 4, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2b2o$bo$o!

Can we count infinite growth in this thread?
Why shouldn't we?

Code: Select all

#c my reason in a nutshell
x = 19, y = 16, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o12$bo15bo$3o3b3o2b3o2b3o$bo15bo!

[dani]

Better mcps=4:

Code: Select all

x = 4, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2b2o$bo$o!

It's equivalent to this MCPS3:

Code: Select all

x = 4, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2bo$bo$o!

[Moosey]

Better mcps=4:

Code: Select all

x = 4, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2b2o$bo$o!

It's equivalent to this MCPS3:

Code: Select all

x = 4, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2bo$bo$o!

Exactly; the mcps = 4 coolcreeper had apparently lasted less than that MCPS3 so I was trying to point out that there are better ones that are trivial-ish to obtain.

[toroidalet]

Can we count infinite growth in this thread?
Why shouldn't we?

The more exotic types of infinite growth you allow, the more problematic the definition of "stabilizes" gets. Already with just puffers, it gets fuzzy if and when puffers stabilise. Is it when they first emerge or when row x becomes periodic or when its debris sequence becomes periodic (and it gets hard to tell, especially with complex ones in S4i rules). Relax the definition a little more and you start getting patterns (like interacting replicators) that appear to stabilise but flare up every once in a while.

Also, in my mind it just doesn't feel... NATURAL... (laughs in silence)

[Moosey]

Can we count infinite growth in this thread?
Why shouldn't we?

The more exotic types of infinite growth you allow, the more problematic the definition of "stabilizes" gets. Already with just puffers, it gets fuzzy if and when puffers stabilise. Is it when they first emerge or when row x becomes periodic or when its debris sequence becomes periodic (and it gets hard to tell, especially with complex ones in S4i rules). Relax the definition a little more and you start getting patterns (like interacting replicators) that appear to stabilise but flare up every once in a while.

I feel that counters and wickstretchers should be accommodatable.
This stabilizes at gen 553 for instance.

Code: Select all

x = 19, y = 15, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o4$bo15bo$3o13b3o$bo15bo7$6b3o2b3o!

[melwin22]

MCPS=2, L=672 (infinite growth, but linear - and it's very easy to find when it becomes regular)

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4acjkw5cny/S12-e3jkr4artw5jy6
bo$o!

More complicated regularization (maybe it's better word than "stabilization" in this case), but also linear growth; L=3695

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4acjkw5y7/S12-e3jkr4aertw5jry6
bo$o!

Even worse (quadratic growth), but it's rather clear that pattern regularizes after about 8160 gens

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4acjkw5cny/S12-e3jkr4aejrtw5jry6
bo$o!

I'm trying to find smth that surpasses L=92 and does not grow to infinity, but I'm constantly failing

Here is a close attempt:

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4acjw5cny7e8/S12-e3jkry4artw5nry6-ek
bo$o!

EDIT: I've actually done it (MCPS=2, L=141)

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4acjw5ny6a7e8/S12-e3jkry4artw5nry6-ek
bo$o!

[CoolCreeper39]

EDIT: I've actually done it (MCPS=2, L=141)

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4acjw5ny6a7e8/S12-e3jkry4artw5nry6-ek
bo$o!

Nice.

[2718281828]

Well done.
Slightly better:

Code: Select all

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

L=154, for MCPS=2.

There are likely better ones.

Edit1:
This is failed, looks promising for up to 230:

Code: Select all

x = 2, y = 2, rule = B1e2i3cky4ajw5n7c8/S12-e3jkr4artw5ry6acn
o$bo!

[CoolCreeper39]

This should last 98,975,173 generations for MCPS=5:

Code: Select all

x = 5, y = 3, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2b3o$bo$o!

98,975,157 for MCPS=6:

Code: Select all

x = 4, y = 4, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
2bo$bo$o$3bo!

98,975,173 for MCPS=7:

Code: Select all

x = 6, y = 4, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
o$3b3o$2bo$bo!

MCP=8+ can be trivially constructed in the same way.

EDIT: Better MCPS=6:

Code: Select all

x = 4, y = 4, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
3bo2$bobo$o!

[CoolCreeper39]

This MPCS=5 methuselah is still going after 10,000,000 generations, and may break the record:

Code: Select all

x = 5, y = 5, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
4bo$3bo$2bo$bo$o!

[Hdjensofjfnen]

This MPCS=5 methuselah is still going after 10,000,000 generations, and may break the record:

Code: Select all

x = 5, y = 5, rule = B2-a3-any5ainy678/S2ce3any4aenyz5kr6-e8
4bo$3bo$2bo$bo$o!

That may potentially be explosive, which makes it void for the purposes of this thread. Although if it does stabilize, we probably have a winner.

Also, the record for MCPS=60 is upwards of 2^74 generations:
http://conwaylife.com/forums/viewtopic. ... start=1325

[CoolCreeper39]

Also, the record for MCPS=60 is upwards of 2^74 generations:
http://conwaylife.com/forums/viewtopic. ... start=1325

Doesn’t that pattern explode?

[Moosey]

Also, the record for MCPS=60 is upwards of 2^74 generations:
http://conwaylife.com/forums/viewtopic. ... start=1325

Doesn’t that pattern explode?

No, it (probably) stabilizes into linear growth. Unfortunately for some unfortunate reason (which has been explained) linear growth is disallowed.
However, I recently posted tetrationally long-lived methuselahs in a related rule which also stablilize into linear growth. They can be easily modified to last far longer than those old 2^500 gen or whatever methuselahs by toroidalet--and they certainly stablilize.

Aforampere also posted this in this thread:

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!

However 27,871,939,396,739,043,039,106 is a lot larger than 7,925,984,864,249,960.

Anyways, a sample of my tetrationally long-lived methuselahs:

Code: Select all

#C lifespan > Googolplex, I think. But definitely less than googolduplex (aka googolplexian).
x = 19, y = 16, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o12$bo15bo$3o3b3o2b3o2b3o$bo15bo!

[CoolCreeper39]

Also, the record for MCPS=60 is upwards of 2^74 generations:
http://conwaylife.com/forums/viewtopic. ... start=1325

Doesn’t that pattern explode?

No, it (probably) stabilizes into linear growth. Unfortunately for some unfortunate reason (which has been explained) linear growth is disallowed.
However, I recently posted tetrationally long-lived methuselahs in a related rule which also stablilize into linear growth. They can be easily modified to last far longer than those old 2^500 gen or whatever methuselahs by toroidalet--and they certainly stablilize.

Aforampere also posted this in this thread:

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!

However 27,871,939,396,739,043,039,106 is a lot larger than 7,925,984,864,249,960.

Anyways, a sample of my tetrationally long-lived methuselahs:

Code: Select all

#C lifespan > Googolplex, I think. But definitely less than googolduplex (aka googolplexian).
x = 19, y = 16, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o12$bo15bo$3o3b3o2b3o2b3o$bo15bo!

What’s the formula for calculating those?

[Hdjensofjfnen]

Anyways, a sample of my tetrationally long-lived methuselahs:

Code: Select all

#C lifespan > Googolplex, I think. But definitely less than googolduplex (aka googolplexian).
x = 19, y = 16, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o12$bo15bo$3o3b3o2b3o2b3o$bo15bo!

Hmm. Looking at it, we need 5 cycles to bump the lateral chain of dominoes into the crosses, so that would take 2^(2^16380 - 16382) generations. I'm not sure what happens after the lateral chains bump into the crosses, but the time for the binary counter to degenerate into a linear growth/spaceship would be quite noticeable.

[Moosey]

Anyways, a sample of my tetrationally long-lived methuselahs:

Code: Select all

#C lifespan > Googolplex, I think. But definitely less than googolduplex (aka googolplexian).
x = 19, y = 16, rule = B2a3ijry4ity5ey/S3i4ent5er6i
9b2o$9b2o12$bo15bo$3o3b3o2b3o2b3o$bo15bo!

Hmm. Looking at it, we need 5 cycles to bump the lateral chain of dominoes into the crosses, so that would take 2^(2^16380 - 16382) generations. I'm not sure what happens after the lateral chains bump into the crosses, but the time for the binary counter to degenerate into a linear growth/spaceship would be quite noticeable.

The crosses are positioned one gen "apart" and they promptly kill the chains. There is then an additional round of counting, so we get to 2^^6 gens, which is >>googolplex (as was mentioned in the comments in the RLE).