Abstract
We consider tiling models of “round quasicrystals” which would have diffraction patterns which are fully rotation invariant—rings instead of Bragg peaks. They can be distinguished from glasses by self-similarity of the pattern of radii of the rings.
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REFERENCES
D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Metallic phase with long-ranged orientational order and no translational symmetry, Phys. Rev. Lett. 53:1951–1953 (1984).
D. Levine and P. J. Steinhardt, Quasicrystals: A new class of ordered structures, Phys. Rev. Lett. 53:2477–2480 (1984).
A. Mackay, Crystallography and the Penrose pattern, Physica A 114:609–613 (1982).
C. Radin, Symmetry and tilings, Notices Amer. Math. Soc. 42:26–31 (1995).
C. Radin, Miles of Tiles, Stud. Math. Lib., Vol. 1 (Amer. Math. Soc., Providence, 1999).
N. G. de Bruijn, Algebraic theory of Penrose's non-periodic tilings of the plane, I, Kon. Nederl. Akad. Wetensch. Proc. Ser. A 84:39–66 (1981).
T. Q. T. Le and S. Piunikhin, Local rules for multi-dimensional quasicrystals, Diff. Geom. Appl. 5:13–31 (1995).
C. Radin, The pinwheel tilings of the plane, Ann. Math. 139:661–702 (1994).
J. H. Conway and C. Radin, Quaquaversal tilings and rotations, Inventiones Math. 132:179–188 (1998).
M. Gardner, Extraordinary nonperiodic tiling that enriches the theory of tiles, Sci. Am., 110–119 (December 1977).
C. Goodman-Strauss, Matching rules and substitution tilings, Ann. Math. 147:181–223 (1998).
C. Radin, Space tilings and substitutions, Geometriae Dedicata 55:257–264 (1995).
S. Dworkin, Spectral theory and x-ray diffraction, J. Math. Phys. 34:2965–2967 (1993).
C. Radin, Symmetry of tilings of the plane, Bull. Amer. Math. Soc. 29:213–217 (1993).
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Radin, C. Symmetries of Quasicrystals. Journal of Statistical Physics 95, 827–833 (1999). https://doi.org/10.1023/A:1004516030941
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DOI: https://doi.org/10.1023/A:1004516030941