A QCA in 2 + 1 and 3 + 1 dimensions

A quantum cellular automaton (QCA), originally proposed as a 1 + 1D confined automaton to model quantum mechanical type behavior, is further extended in this paper to 2 + 1 and 3 + 1 dimensional confinements. QCA trajectories are fractal-like in space and time and can be characterized by a fractal dimension d distinct from its topological dimension D. In addition, QCAs have the pronounced feature of having single space time swaths which are continuous, though non-differentiable, over recurrence cycles in most cases of interest. This unique feature leads to identifying angular momentum states with the quasiparticle ‘anyons’ in 2 + 1D and hydrogen-like orbitals in the 3 + 1D case. It also emerges from identifying QCA states with actual physical orbitals that properties such as spin and magnetic moments are no longer ‘intrinsic’ to orbital electrons but features of QCA/fermion space-time behavior in a fashion similar to the other orbital quantum numbers.