John G
The Living Force
Fractals have more uses than just modeling QM, I don't think Ark is saying all his fractals are physically realistic, you kind of want your discrete structure in spacetime to be 4-dim or 3-dim for space. Given that Ark is using conformal transformations, he has torsion I would think and the following may apply:My point was that homotopy spheres (your S^2 and S^3 manifolds) don't have anything to do with fractal dynamics since S^2 or S^3 manifolds don't support (non-trivial) Hamiltonian flows (which are required to write any Lagrangian for QM)...Also, S^3 manifolds shouldn't be used because of the zero divisor problem (That's why Hamilton invented quaternions!) unless you're very sure you're in a zero torsion environment (eg infinitely thin disk gyro, or Gibbs' vector space EM theory, etc).
The compact manifold that represents 4-dim spacetime is RP1 x S3, the Shilov boundary of the bounded complex homogeneous domain that corresponds to Spin(6) / (Spin(4)xU(1)).