Hi Michael
Thanks for your kind comments about the fqxi essay. You correctly evaluate my BU model as a species of cellular automata (CA). I sometimes think of it as a sort of self-operating 3D abacus inasmuch as self-assembly creates a lattice structure. In the original CA the only 'action' involved is a two-state on-off for each cell. You mentioned that 7 dimensions are required by physics - I would be grateful for an online reference about this to study.
In my Beautiful Universe (BU) nodes there are the following degrees of freedom: 1-rate of rotation or spin of a node in units of (h). 2- two degrees of freedom in the orientation of a cell in spherical coordinates. I wonder how these would count in terms of 'dimensions'. I also feel that the usual 3 spatial and one time dimension are emergent from the node interactions themselves. You have diagnosed exactly what is needed in my theory: As to geometry I think a face-centered-cubic (FCC) lattice is a reasonable starting point ( adopted over the other Kepler packing, following N. Cook, see below). The update rules still need to be to be quantified. Although it is not exactly a BU 'particle' treating three nodes as bar magnets interacting classically lead to a model one aspect of the Strong Force so the rule required may be similar in BU.
Yes The Uncertainty relations in CA emerge exactly are as you stated them. In the case of the two overlapping cells you describe it will be just like the Airy diffraction limit! I strongly feel that orderly diffraction (ie diffusion) in a lattice is the cause of both uncertainty and probability in QM. In Fig. 29 of (BU) you can see how this is illustrated in 2D (the case you describe) and also in a 3D lattice. The trouble of considering KK in BU is that it is a sort of an add-on to Special Relativity's 4-D spacetime. In BU I totally ignore SR as a starting point and think that discrete Lorentz transformations in an absolute universe are enough to describe relativity in the lattice.
By the way Fig. 16 of BU which you referred to is from my friend Norman Cook's work. I told him about the fqxi contest and he has contributed a very thorough explanation of his FCC-based nuclear structure theory. More support for our sort of approach to physics, so please encourage his work.
I will have to re-read your essay and think about the interesting points you raised including your fascinating conclusion that Gödel's theorem has applications in basic physics!
With best wishes,
Vladimir