Are there methuselas that are known to be not glider-constructible?

For general discussion about Conway's Game of Life.
Post Reply
tcorlett
Posts: 1
Joined: July 25th, 2022, 2:40 pm

Are there methuselas that are known to be not glider-constructible?

Post by tcorlett » July 25th, 2022, 2:46 pm

I saw a tweet about the non glider-constructible still life. I was wondering if the same is true with some methuselas?
Or really, any oscillators or structures that are not "still" regardless of their longevity.

I just joined the forum out of curiosity - my knowledge of Game of Life structures is very basic. Forgive me if the question is ill posed or non-sensical.

hotdogPi
Posts: 1587
Joined: August 12th, 2020, 8:22 pm

Re: Are there methuselas that are known to be not glider-constructible?

Post by hotdogPi » July 25th, 2022, 2:51 pm

Yes. Most Gardens of Eden just look like random blobs; the ones that were stable were major discoveries.
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,47,48,54,56,72,74,80,92,96S
217,486,576

S: SKOP
G: gun

User avatar
dvgrn
Moderator
Posts: 10612
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI
Contact:

Re: Are there methuselas that are known to be not glider-constructible?

Post by dvgrn » July 26th, 2022, 8:25 am

hotdogPi wrote:
July 25th, 2022, 2:51 pm
Yes. Most Gardens of Eden just look like random blobs; the ones that were stable were major discoveries.
And while most random blobs aren't methuselahs, for any given definition of "methuselah" you can pretty much pick any Garden of Eden, write a program to randomly scatter more ON cells around its edges and see how long the resulting blob lasts, and you'll eventually find a methuselah (that is still a Garden of Eden, because you didn't change the original Garden of Eden part).

dani
Posts: 1222
Joined: October 27th, 2017, 3:43 pm

Re: Are there methuselas that are known to be not glider-constructible?

Post by dani » July 29th, 2022, 7:06 pm

tcorlett wrote:
July 25th, 2022, 2:46 pm
...any oscillators or structures that are not "still" regardless of their longevity.
Of note is Unsynthesizable oscillator 1, which is a period 2 structure that cannot be synthesized. It didn't get as much coverage but is still pretty fascinating. It was found using a similar method to the discovery of the still life, soon after.

We don't know if any spaceships are unsynthesizable, but it's theorized that large, blobby spaceships like Sir Robin don't have a synthesis due to the chaoticness of their form, and how many gliders you'd have to pack together to keep it stable. I'm not sure if one could be explicitly proven along the lines of the still life and oscillator, but it doesn't seem too unlikely.

Post Reply