Perhaps assign each co-ordinate to musical notation and you can get some Scheonberg-esque compositions

Random walk is definitely possible. Also possible that we're observing some "search" in the embedding space from an initial point. It's hard to tell because the chains are often similar lengths, so I don't think it really terminates early. It might be interesting to find the closest CoT component to the final answer and see how step distance inflects at that point