Very interesting observations! How did you stumble on this? :-)

IIUC (based on one of your blog comments), you typically need one “immediate” neighborhood and one “ring-like” neighborhood further away. The latter seems like it might likely require non-locality in a fundamental sense (which typically leads to both philosophical and practical problems, like how do you keep the non-locality in check to maintain approximate locality). Any thoughts on that?

Those NH configurations were simply examples, I've used a wide variety of randomly generated NHs and they all have their own quirks and capabilities.

Could you clarify what you mean by non-locality? All NHs are a circle, or ring(s) of pixels around the 'origin' pixel [0, 0]

Really enjoyed it.

Only thing I would add is numbering and rules for the extra videos. Easier to talk about that way (e.g. "I wonder what's going on with discrete pattern #7).