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Methulesahs with the biggest final populations

Posted: June 1st, 2024, 3:36 pm

by Azerty

Hello, I created this topic because I wanted to make a list of the n cell pattern that make the biggest final population in cells.

If you discover a pattern that could replace another pattern or get added to the list, you can submit it below by putting it's RLE text.

Here are the rules:
- Infinitely growing patterns are not allowed, except if they eventually get destroyed (eg. a glider hit the engine).
- Only the final population count. The lifespan and the hitbox don't matter.
- The starting pattern must fit in a n x n bounding box where n is equal to the number of cells the pattern contains.
The maximum bounding box size is here to prevent people from building an infinite growing machine and put a stable pattern very far away to destroy it.
- If the final population contains oscillators or spaceships that change population (eg pulsars), only the maximal population, the minimal population does not.

Current winner patterns and their final population cells count:
1. 0
2. 0
3. 4 cells (pre-block)

Code: Select all

x = 2, y = 2, rule = B3/S23
o$2o!

4. 12 cells (T-tetromino)

Code: Select all

x = 3, y = 2, rule = B3/S23
3o$bo!

5. 116 cells (R-pentomino)

Code: Select all

x = 3, y = 3, rule = B3/S23
o$3o$bo!

7. 633 cells (acorn)

Code: Select all

x = 7, y = 3, rule = B3/S23
bo$3bo$2o2b3o!

8. 952 cells

Code: Select all

x = 6, y = 4, rule = B3/S23
4bo$4b2o$2ob2o$o!

9. 1744 cells (bunnies)

Code: Select all

x = 8, y = 4, rule = B3/S23
4bobo$obo2bo$bo3bo$bo5bo!

11. 2898 cells

Code: Select all

x = 8, y = 5, rule = B3/S23
7bo$obo2b2o$o5bo$3bo$b3o!

13. 5151 cells

Code: Select all

x = 8, y = 7, rule = B3/S23
6bo$3bobo$o4bo$b2o$2bobo$3bo$5b3o!

23. 13959 cells

Code: Select all

x = 14, y = 16, rule = B3/S23
5b4o$9bo$9bo$10b2o6$o$o$o$b2o$b3o7b3o$b2o7bo$10bo!

25. 57646 cells

Code: Select all

x = 16, y = 15, rule = B3/S23
5b4o$9bo$9bo$10b2o4$13b3o$15bo$o13b2o$o12bo$o$b2o$b3o$b2o!

27. 17954325 cells

Code: Select all

x = 23, y = 21, rule = B3/S23
6bobo2$5bobob2o$11bo2$11b2o5$bo$obo$19bobo$o2bo18bo$2b2o14bo2bo$3bo14b
2o3$16bo$16bo$16bo!

Re: Biggest cells count from final population possible to get starting with n cells

Posted: June 1st, 2024, 3:48 pm

by confocaloid

Azerty wrote: June 1st, 2024, 3:36 pm I created this topic because I want to make a list of the n cell pattern that make the biggest stage population in cells.
[...]

Looking through List of long-lived methuselahs, here are some candidates:

multum in parvo, acorn: initial population 7, final population 633
7468M: initial population 8, final population 952
Bunnies: initial population 9, final population 1744
initial population 10, final population 3611:
dani wrote: March 17th, 2022, 3:28 am[...]
Code: Select all
```
x = 39, y = 78, rule = B3/S23
3o2b2o$3bo$5bo75$36b3o!
```
[...]
24827M: initial population 13, final population 5151

Re: Biggest cells count from final population possible to get starting with n cells

Posted: June 1st, 2024, 4:02 pm

by Azerty

confocaloid wrote: June 1st, 2024, 3:48 pm
Azerty wrote: June 1st, 2024, 3:36 pm I created this topic because I want to make a list of the n cell pattern that make the biggest stage population in cells.
[...]
Looking through List of long-lived methuselahs, here are some candidates:
multum in parvo, acorn: initial population 7, final population 633

7468M: initial population 8, final population 952

Bunnies: initial population 9, final population 1744
initial population 10, final population 3611:
dani wrote: March 17th, 2022, 3:28 am[...]
Code: Select all
x = 39, y = 78, rule = B3/S23
3o2b2o$3bo$5bo75$36b3o!
[...]
24827M: initial population 13, final population 5151

I added the 24827M pattern but I didn't added the 10 cells one because the bounding box of is too large.
The acorn, the 7468M and the bunnies were already in the list.

Re: Methulesahs with the biggest final populations

Posted: August 21st, 2026, 8:37 am

by g0t0

What about this:

Code: Select all

x = 235, y = 189, rule = B3/S23
28$52bo$52b2o111$175bo$173bob2o$173bobo$173bo$171bo$169bobo!

for >12, it is infinite.

Re: Methulesahs with the biggest final populations

Posted: August 23rd, 2026, 4:29 pm

by melwin22

g0t0 wrote: August 21st, 2026, 8:37 am What about this:
Code: Select all
x = 235, y = 189, rule = B3/S23
28$52bo$52b2o111$175bo$173bob2o$173bobo$173bo$171bo$169bobo!
for >12, it is infinite.

This was specifically disallowed by rule 3. It has a bounding box much larger than 13x13.

Re: Methulesahs with the biggest final populations

Posted: September 21st, 2026, 1:40 pm

by edtoml

Fits in a 20x20 rectangle, runs for about 126 million generations before stabilizing.

Code: Select all

5b4o$9bo$9bo$10b2o6$o$o$o10b2obobo2bo$b2o14bobo$b3o8b3o3b2o$b2o8b4obo
2bo$11bobo4bo$17b3o$14bobo2bo$11b2ob3obo$12b3ob4o!

if Rustylife counts correctly, the ending population is 17,954,309

Re: Methulesahs with the biggest final populations

Posted: October 7th, 2026, 4:10 am

by 2718281828

Code: Select all

x = 7, y = 5, rule = B3/S23
3o$o2bo3$4b3o!

8cells init, final population 1342

Re: Methulesahs with the biggest final populations

Posted: October 7th, 2026, 9:30 pm

by squareroot12621

2718281828 wrote: October 7th, 2026, 4:10 am
Code: Select all
x = 7, y = 5, rule = B3/S23
3o$o2bo3$4b3o!
8cells init, final population 1342

Final population 1504 (stabilizing at generation 11238):

Code: Select all

x = 31, y = 25, rule = B3/S23
3o22$28bo$28b3o$29bo!

I’m currently running a Python program to find 8-cell methuselahs like this.

Edit: I didn’t see the bounding box rule. I’ll keep running the search anyway, because it’s not trying to find infinitely extensible methuselahs. ⵌmethuselah ⵌpopulationˍ8 ⵌfinalˍpopˍ1504 ⵌlifespanˍ11238

Re: Methulesahs with the biggest final populations

Posted: October 7th, 2026, 9:37 pm

by Andrew

edtoml wrote: September 21st, 2026, 1:40 pm Fits in a 20x20 rectangle, runs for about 126 million generations before stabilizing.
Code: Select all
5b4o$9bo$9bo$10b2o6$o$o$o10b2obobo2bo$b2o14bobo$b3o8b3o3b2o$b2o8b4obo
2bo$11bobo4bo$17b3o$14bobo2bo$11b2ob3obo$12b3ob4o!
if Rustylife counts correctly, the ending population is 17,954,309

Confirmed using Golly.

Re: Methulesahs with the biggest final populations

Posted: October 8th, 2026, 12:37 pm

by squareroot12621

The best 8-cell methuselah, according to my search, has a final population of 2464 (lifespan 12505):

Code: Select all

x = 55, y = 64, rule = B3/S23
54bo$54bo$54bo59$o$3o$bo!

This one didn’t win, but it did make two lightweight spaceships:

Code: Select all

x = 15, y = 28, rule = B3/S23
12bo$12b3o$13bo23$o$o$o!

I also saw 8-cell methuselahs with mirrored tables, mirrored buns, heavyweight spceships, and integrals.

The search took about 3 hours to run, plus 15 minutes to catch some of the bugs my original program had. It’s not comprehensive (or very complicated, for that matter), but it should have found most of the methuselahs with the largest ash.ⵌmethuselah ⵌpopulationˍ8 ⵌfinalˍpopˍ2464 ⵌlifespanˍ12505

Re: Methulesahs with the biggest final populations

Posted: October 9th, 2026, 3:15 am

by HartmutHolzwart

I was always wondering whether another „near-puffer-engine“ hides in such long running methuselahs and whether we would ever be able recognize it when it occurs. So something like a switch engine, only larger and easy to destroy because of a long cycle.

By now, billions of apgsearch runs would have identified any such engine, wouldn‘t they?