I don’t think Turing-completeness implies omniperiodicity. I’m imagining a cellular automaton which follows Game of Life rules on even-numbered generations and does nothing on odd-numbered generations, which is trivially Turing-complete because it’s just Conway’s Game of Life if you ignore every other generation, but also trivially has no odd-period oscillators.
Hermitcraft? Seems hard seeing as the subreddit is about as official as it can get short of being literally, officially run by the Hermits. I can’t imagine a Lemmy community would see any significant amount of participation except for some number of people double-posting in both. I’d be happy to be wrong though.