Multidimensional "paperfolding" Structures - Three and Four Dimensions

We recapitulate our previously developed recursive algorithm for creating "paperfolding" structures in arbitrary dimensions. Here we explain and apply it specifically to three and four dimensions. We visualize the results by suitable projections. We also explicitly enumerate the number of "folds" in the first four generations of the recursion. We conjecture (without proof) that the Fourier spectrum of the structures is pure point (the Bragg peaks).