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It's interesting how some of them halt after a while and some of them don't. I wonder if one could figure out which ones do and which ones don't?

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None of them halt, since no halting state is ever introduced into these canvas dwelling TMs :-(

I think GP is actually asking whether we can determine if one enters a steady state, i.e. tape no longer changes.

You are kidding, right? [0]

[0] https://en.wikipedia.org/wiki/Halting_problem

These are FSMs though, as the tape is finite.

It was a (not particularly funny) joke.

I thought it was great :)

It was fine. The combination of difficulty detecting humor or sarcasm, a need to geek-preen, and limited filter can sometimes result in unfriendly or unwelcoming comments.

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