Multidimensional "Paperfolding" Structures - Three and Four Dimensions

S.I. Ben-Abrahama, D. Floma, R. Richmana and D. Shapirab aDepartment of Physics, Ben-Gurion University of the Negev, POB 653, IL-84105 Beer-Sheva, Israel bThe Racah Institute of Physics, The Hebrew University, IL-91904 Jerusalem, Israel

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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).

DOI: 10.12693/APhysPolA.126.435 PACS numbers: 61.44.Br