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Over the years I’ve studied the simplest ordinary Turing machines quite a bit, but I’ve hardly looked at multipath Turing machines (also known as non-deterministic Turing machines, or NDTMs). Recently, however, it became clear to me that reusable Turing machines can be viewed as “maximally minimal” models both for computing at the same time and for the way we think about quantum mechanics in our physics project. Now this piece is my attempt at “doing the obvious explorations” of reusable Turing machines. And, as I’ve found so many times in the computing universe, even cases with some of the simplest rules bring some significant surprises …

Ordinary vs. reusable Turing machines

An ordinary Turing machine has a rule like



This gives a unique successor for each configuration of the system (here it is shown how the page goes down the page from an initial state consisting of an empty band):


RulePlot[TuringMachine[2506] , {{1, 6}, Table[0, 10] 


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