Thank you Jonathan. I read your comments above about quatrenons and, as with Colin, the necessity of having 7 dimensions and 't Hooft's comments about CA. As you have probably figured by now I am still a learner! At 70 I am not as mentally agile as I was when I first started my physics self-study, but with so many wonderful contacts on the Internet, and through discourse with first-class thinkers here and elsewhere I could see where and how my model agrees or does not with other established theories and ideas, and will be mulling all these things and adjusting my model accordingly.
Quatrenons or octonons might be the answer but I know my own mind - I simply do not think algebraically, and would rather use the energy required to learn them to work things out geometrically and leave it to you whizzes (Colin included) to establish the math for such ideas.
I wonder if the 7 symmetries required are all 'basic'. In my Beautiful Universe theory I have seen how leaving special relativity (i.e. c constant and the use of 'spacetime' as a starting premise) out of GR can lead to an utterly simply scenario of space with a density matrix refracting e/m energy. If that is indeed so, I sincerely hope that some such simplifications in assumptions (as per my fqxi essay 'Fix Physics!' could one day show that the required symmetries are emergent from the simple symmetries of a model like BU.
I looked up Lorentz Invariance..more things to study. I do not know which CA 't Hooft had in mind, but surely there are many different models that use discrete self-assembled nodes? If he thinks of CA as simple 'on' off' nodes then yes I agree, but in my BU the nodes have these degrees of freedom: A scalar internal rotation ie density a 2- dimensional spherical orientation that should include ( -) spin orientation, apart from the 3 dimensions of their location in the grid . That is six, will that work? OK nice try perhaps but I am thinking a lot about other possibilities. I am now considering the concept of spherical surfaces in the lattice where the nodes are aligned 180 degrees twisted in relation to and caused by the original 'locked' matter nodes. Atoms as black holes...a google shows the atom as a black hole is by no means a new idea!
By the way I think the Einstein quote in your slide may have been the old chestnut (I paraphrase from memory ) about any fool thinking he knows what a photon is, but it is still a mystery.
Yes Ste*ve is irritating - his rambling off-subject comment was inappropriate, but you were more tolerant and generous by offering your Dante quote.
Best wishes and appreciation, Vladimir.