What is the simplest example of a rewriting system from binary strings to binary strings
that can perform universal computation? Binary string rewriting systems in general can compute any computable function, but I have trouble finding particular instances that can by themselves compute any computable function given an appropriate input. I've seen statements that a class of rewriting systems (e.g., the set of cyclic tag systems) is Turing-complete, but I'm looking for a single rewriting system that is universal.
I was thinking a self-modifying bitwise cyclic tag system might be a candidate, but I'm not sure how to interpret the output of such a system.