[breck]

> Is there some obvious way of generalizing the 1d rules to 2d that I'm missing?

No you are correct. I was looking for analogies, to help me flush out my thinking of the space more by looking at it from a few angles.

I wanted to think about systems of limited size or machines of different dimensions but turns out periodicity is known for those (https://www.wolframscience.com/nks/p255--systems-of-limited-...).

My main attack vector is to build up a simple new math starting with just 1 and 0 to define both the problem and solution in and see where it goes, hopefully creating useful side effects along the way. If I were to solve a problem my hunch is it will be related to impossibilities in formally defining "infinite sequence" in the problem definition in such a language.