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‘‘Game of Lie” Cellular Automaton of Periodic Table Crystallization in Killing Root Space A2/A3 .
erik trell

Last modified: 2020-02-17


Simple considerations such as “here, in this spot of Universe where we are today innumerable other things will take place over the years”, infer that three-dimensional Euclidean space, always remaining there, is timeless. Likewise, if with Ptolemy we as a direct parametrization span a grid of perpendicular straight lines over the space, every so shaped cubical or other parallelepiped ‘cuBit’ cell in it will contain and thus distribute the same timelessness isotropically. A direct Lie algebra SU(3) phase transition of these cells from a cubical to a spherical infinitesimal generator symmetry by a sequentially space-filling R3×SO(3) wavepacket cellular automaton projection of its “straight line of length equal to zero” eigenvector hierarchically crystallizes  the  successive stages of the atom and periodic table geodesics all at the same instant. But without a genuine temporal degree of freedom exactly the same spot cannot be occupied more than once, posing the dilemma: either our realization exhausts its space slot or, like when ice at once freezes in complicated whorl and backflow patterns, may have left neighboring recesses behind which might be filled up, perhaps even by us, in another apparent time relation.