  Multiway Turing machines (also known as nondeterministic Turing machines or
NDTMs) with explicit, simple rules are studied. Even very simple rules are
found to generate complex behavior, characterized by complex multiway graphs,
that can be visualized in multispace that combines "tape" and branchial space.
The threshold for complex behavior appears to be machines with just s = 1 head
states, k = 2 tape colors and p = 3 possible cases, and such machines may
potentially be universal. Other characteristics of multiway Turing machines are
also studied, including causal invariance, cyclic tapes and generalized busy
beaver problems. Multiway Turing machines provide minimal examples of a variety
of issues encountered in both concurrent computing and the theory of observers
in quantum mechanics, especially in our recent models of physics.
