Hi Russel,
You are right, running programs is the way forward. Physicists seek simple static formulae, but Nature doesnt work that way. It is dynamic and efficient. We should use simple recursive programs, like Mandelbrot's, and a language like Lisp, to reflect it.
This model uses a rotating discrete circle. Moving it gives a sine wave formula, Schroedingers equation is an expanding spherical wave, and after that the formulas get too hard. But simulations can still run such "unsolvable" problems, e.g. traffic simulations, given valid simplifying assumptions. But we are like the man looking for his keys under a lamp post, who when asked where he lost them said "In the bushes, but the light is better here", e.g. we assume a flat 3D Euclidian space when we know space curves; we assume triangular spin networks when even war gamers use hexagons not squares, to get more movement directions; we assume static links when even New York cell phone networks dynamically reorganize links under load. Yet it is possible, e.g. Bruce Maiers simulations using "boxel" cubes, see LINK .
Can we do on classical computers what nature does with quantum computing? Prime numbers that supercomputers take hundreds of years to find take only seconds on a quantum computer. Yet the model does suggest simplifying assumptions, e.g. that there are only four dimensions, that all node transfers use planar channels, with a finite capacity exactly equal to the total processing of any photon. The theory also explains why it is so hard to simulate even what a single photon does - because it distributes its processing to literally travel every possible path, even though it restarts at a node point when detected (See LINK Ch3, p19, The law of least action). I am jumping ahead a bit, but consider why the mass of an electron or neutrino etc is always a value range, but their charge is an exact value. In this model, the charge processing remainder after a channel overload is exact, while the mass is the processing the node does before it overloads varies with channel processing order effects.
So I think yes, it is possible, but realistically we are not too far down that track at present.
all the best
Brian