So, @wryl, who created Modal, demonstrated to me an interesting connection between Fractran and rewriting programming languages that I couldn't see at first. It is not obvious until you point the registers to symbols in memory, but once named registers defined in rules start to be rewritten, it suddenly becomes obvious that this a very powerful OISC(where the only instruction is Multiply) rewriting engine system, moreso than Thue if I dare say:
Here's an example run:
:: 5/6 blue.2 red.3 > purple.5
:: 11/21 yellow.7 red.3 > orange.11
AC 126 blue red red yellow
00 126 × 5/6 = 105/1, red purple yellow
01 105 × 11/21 = 55/1, purple orange