[andrewla]

> 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?

[biggiemac42]

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.

[dvgrn]

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.