Stephen Wolfram has begun exploring multiway Turing machines, also known as nondeterministic Turing machines (NDTMs). These machines, which allow for multiple possible outcomes from a given state, are seen as "maximally minimal" models for both concurrent computing and quantum mechanics in Wolfram's Physics Project.

Unlike ordinary Turing machines with a single successor for each configuration, multiway Turing machines can have rules specifying multiple outcomes. This results in a branching evolution, visualized as a multiway graph. Wolfram's exploration focuses on the behavior of multiway Turing machines with simple rules, comparing them to ordinary Turing machines where the threshold for computational universality is demonstrated to be s = 2, k = 3.

The study delves into the threshold for universality in multiway Turing machines and examines rules with subsets of possible cases, leading to halting or non-halting behaviors. Simple multiway Turing machines with just two cases in their rules can generate complex patterns, such as infinite binary trees or graphs where branches terminate under specific conditions. As rules become more complex, with 3 cases, the multiway graphs can exhibit intricate structures, including states appearing at multiple steps and actual loops, indicating more complex computational behavior.