It does match. & that it can match is what matters. It shows how the salient aspects of our universe or models of physics might arise from simple rules.

No, it doesn't show how and you didn't show how it matches. I've read from your other comments that you are big fan of "internal meanings". We humans use language to communicate ideas so that we can connect your internal meanings to everyone's internal meanings, but you didn't present any meaningful connection between those DFA and real physical processes, or at least any connection that someone interested in this topic could see. I understand what you write in the article, but I can't see any match between those DFA's and physics. Make any sensible example and then we can talk.