Originally I wanted to make a point here about Interactive Computation, the strong Church-Turing hypothesis and persistent Turing Machines, however, while checking on the latest research in that area before doing so, I found the following paper:

https://arxiv.org/abs/1702.06000 TE Raptis - 'Viral' Turing Machines, Computation from Noise and Combinatorial Hierarchies

Which gets cited by the following paper by the same author, which cites the OP paper(!), AND elaborates on it:

https://arxiv.org/abs/1805.06301 TE Raptis - Finite Information Numbers through the Inductive Combinatorial Hierarchy

Which itself gets yet another follow on by the same author:

https://arxiv.org/abs/1806.01637 - Encoding discrete quantum algebras in a hierarchy of binary words

Highly interesting.