Abstract
Dense square-symmetry tilings of the plane by equilateral triangles and squares are described. Repeated substitution of a vertex of a tiling by groups of vertices leads asymptotically to a limiting density that is independent of the starting pattern and to a family of quasicrystalline patterns with 12-fold symmetry. Diffraction patterns were computed by treating the vertices as point scatterers. As the number of substitutions increases, and as the unit-cell size increases, the diffraction patterns from a single unit cell develop a near-perfect 12-fold symmetry. In addition, the low-intensity background scattering in the diffraction patterns exhibits fractal-like self-similar properties, with motifs of local intensity recursively decorating the more intense features as the number of substitutions progresses.
Original language | English (US) |
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Pages (from-to) | 5-9 |
Number of pages | 5 |
Journal | Acta Crystallographica Section A: Foundations of Crystallography |
Volume | 66 |
Issue number | 1 |
DOIs | |
State | Published - 2010 |
Keywords
- Fourier transforms
- Quasicrystals
- Tilings
ASJC Scopus subject areas
- Structural Biology