@mcc @yala @futurebird - I agree, it would be good to put spin networks on a compute and let them evolve in time and see what they do. We need to accumulate knowledge about such things.
I helped invent "spin foams" because they're a spacetime way of thinking about how spin networks evolve in time. Later @jdchristensen, @gregeganSF and I simulated some on a supercomputer (actually a "Beowulf cluster"), and we learned some stuff, mainly that existing theories of spin foams didn't work the way people were hoping.