Yesterday I posted about Serendipity/Synchronicity in religious terms instead hard-wired archetypes and a math approach to Schemes via Hofstadter and his excellent AI approach which I would describe as elven in Merlin milieu. NonCommutative Geometry and Connes + hep-th/9606001 are resources. A key feature is Penrose tiling which relates to quasicrystals and spontaneous symmetry breaking which links to a random generator and maybe virtual reality. About the tiling:"Every finite patch of tiles in a tiling by kites and darts does occur, and infinitely many times, in any other tiling by the same tiles". This language will support RH logic. The quantum theory closes is Event Symmetric perhaps with strings attached :) I find Euler numbers V-E+F=2; e^(i pi)=-1 and a^{phi (n)}=1 important. Phi is crucial to the construction of the tiling which is also a projection of a 5 dim torus and xray diffraction pattern of 5dim quasicrystal spontaneous symmetry breaking at the vertices. To form a planar graph from a polyhedron use light source on one face of p and a plane on the other side. Noah's Ark Proof. Reminds me of Plato's cave shadows

To sumerize: Finding different categories of behavior in large CA rules spaces such as 8-state, 5 neighbor CA is like solving the construction of Penrose Tiling. A 5dim torus or xray diffraction pattern of a 5dim quasicrystal exhibiting spontaneous symmetry breaking. This is aperiodic which is why I chose the pallendromic Subject CA and AC. It is associated with the Leech lattice E8 or octinion. It is related to the formula for phi square root of 5 plus/minus 1 divided by 2. The Axiom of Choice is base upon well-ordered sets. non well-ordered sets occur at the incidence of chaos which is why the CA rules become hard to compute because of the randomness Penrose tiling:"Every finite patch of tiles in a tiling by kites and darts (oxen and carts) does occur, and infinitely many time in any other tiling by the same tiles See Robertson-Seymour Theorem--The Higgs particle requires AC. As to non-commutative geometry and the event-symmetric structure employing Clifford algebras. "The stepping pro- cess is a form of quantization needing the most general form. The q step will construct an algebra=q reiterated.