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Dear Tommaso:
I think my previous question - or the answer for it- got lost with the answer from an for Constantin.
I think your essay is great and your proposal of identifying space time "atoms" with a cellular automata yet to be debugged and understood is plausible. From experiments - or simulations- like the ones presented in "new kind of science" and in your essay we see "particles" and all sorts of things emerge. We could even find quantum mechanics emerging from there.
As you say, the automata are not yet "seen" and not debugged.
I think - as I propose in my essay- it might also be plausible to search the basic automata on the particles or sub particles instead of in space-time. I identify the basic automata with particles and see space and time derived from the interaction. Unfortunatly I haven't done concrete definitions and experimentation.
I feel my approach may have the problem of having more complex automata but might be easier to codify relativity and quantum mechanics in there.
Now, again, could you comment on the different approaches?. I do believe in an algorithmic universe, as many others -like Hector Zenil- do.
Regards