Any Game of Life pattern can be constructed from just 15 gliders (2022) | Hacker News Reader

Any Game of Life pattern can be constructed from just 15 gliders (2022)

biggieblog.com

47 pointsfanf211 comments

Note: This just says that any GoL pattern that can be constructed by a universal constructor can be constructed from 15 gliders. A universal constructor is a GoL pattern that can construct a very diverse set of patterns, but not any pattern. For example, Garden of Eden patterns are excluded from this category.

> For example, Garden of Eden patterns are excluded from this category.

That seems to be naturally true, since they by definition cannot be constructed. Are there other patterns that cannot be constructed by a universal constructor, or are all such patterns non-constructible?

The post (and my previous waterbear post) both talk about universal construction, it is equivalent to glider construction. There are patterns which have N generations of predecessor but not N+1, which are also non-constructible.

There are also patterns -- both stable patterns and oscillators -- that have an unbounded chain of predecessors, but still can't be glider constructed. That is, there are proven solutions to Conway's "Unique Father Problem" from over half a century ago:

  https://conwaylife.com/wiki/Unique_father_problem

To put it another way, there are certain patterns that, if you see them in the Life grid, you know they've always been there from T=0 -- because they are provably their own only predecessor.

Previous discussion: https://news.ycombinator.com/item?id=33797799

That was a lot to take in. Inspiring.

The last video on the page gives me massive Universal Paperclips vibes.

Sounds fascinating, but unfortunately, I can't read it at the moment. It's serving a 500.

Hi, I'm the author, the preferred URL is https://biggieblog.com/building-arbitrary-life-patterns-in-1.... Does that work for you?

Yes. Thanks!

We'll change to that from https://btm.qva.mybluehost.me/building-arbitrary-life-patter... above. Thanks!

Reply on news.ycombinator.com