Lee,

I'll take a look but first meet me halfway and tell me a little about these things and how you think an implementation might work.

Since this isn't a physics forum it is safe to assume that nobody is an expert, and you are free to keep things at an elementary level.

Here's t'Hooft's paper.

I haven't seen this book, but at the 2015 Wolfram Summer School, Sibesh Kar was working on trying to understand those ideas from the point of view of simple computer experiments like those found in Stephen Wolfram's A New Kind of Science.

There were many directions this project could have gone in because of the wide variety of things t'Hooft was writing about.

It seemed like the type of cellular automaton rule with separate updates on the even cells and the odd cells was a reasonable intersection. t'Hooft has some papers showing how those updates can be analyzed like they were quantum mechanical operators, and at the same time it is possible to find simple rules which are candidates for universal behavior according to Wolfram's Principle of Computational Equivalence.

Here is an example of something Sibesh found, which also happens to be a reversible rule {57,99},

with this update definition

EvenOddUpdate[even_, odd_][init_] := 
 Riffle[CellularAutomaton[odd,  Riffle[init[[1 ;; ;; 2]], 
    #]][[1 ;; ;; 2]], #] &[ CellularAutomaton[even, init][[2 ;; ;; 2]]]

and running this evolution

ArrayPlot[NestList[EvenOddUpdate[57, 99], RandomInteger[1, 400], 400]]