ConwayLife.com

Today I found a way to add another 45 generations to David Bell's version ov Lidka: The lifespan is 29100 generations. Is it the longest lifespan known for a methuselah with 13 or fewer cells?

Is it the longest lifespan known for a methuselah with 13 or fewer cells?

That is indeed the longest-lived 13-cell methuselah in a 13*13 box. (An 8-cell methuselah in a 7500*7500 bounding box could last longer, for instance.)


Anyway, that's cause for celebration!


As for the longest-lived x-cell methuselahs in a x*x box, I believe the records are:

1 1
2 1
3 2
4 10
5 1105
6 1108
7 5206
8 7468
9 17410
10 17423
11 17465
12 23334
13 29100

This is a weakly-increasing uncomputable function, and thus there is no O() bound based on computable functions. It should be possible to impose a limit of O(BB(f(x))), where BB() denotes Rado's 'Busy Beaver' function, but this limit will grow much faster than the actual function for small values of x.

calcyman wrote:As for the longest-lived x-cell methuselahs in a x*x box, I believe the records are:

1 1
2 1
3 2
4 10
...

o$obo$o! lasts for 11 ticks, I believe; the classic T-tetromino lasts 9. Is there a four-cell traffic-light predecessor that lasts exactly 10 generations?

dvgrn wrote:Is there a four-cell traffic-light predecessor that lasts exactly 10 generations?

This 4-cell predecessor lasts 10 generations:

These two predecessors increase the lifespan by one generation while staying within the constraints in Calcyman's post: These two one-generation predecessors result in a smaller bounding box (14*10): I did some limited searching for 2-generation and 3-generation predecessors but was unsuccessful.

Sokwe wrote:These two one-generation predecessors result in a smaller bounding box (14*10)

Or you can arrange the tub and either one of them in an even smaller bounding box (4*20):

The following 3 by 4 pattern that I found a few years ago lasts 1104 generations: So f(4) is substantially higher than Calcyman indicated.

That's a 6-cell pattern so it's a contestant for f(6), not f(4).

Ah, I thought we were just looking at bounding box, now I see that the pattern must have x cells AND be contained in a x by x box...never mind