Juan García Escudero and Javier García García 2005 J. Phys. A: Math. Gen. 38 6525 doi:10.1088/0305-4470/38/29/008
Juan García Escudero1 and Javier García García2
Show affiliationsNon-periodic planar patterns generated by deterministic inflation rules are described. Several types of patterns with both unit and non-unit Pisot numbers as inflation factors are formed by triangular prototiles. When the inflation factor is the silver mean, the patterns can be obtained by superimposing two subpatterns and some of them can be converted into face-to-face patterns. The geometric constructions corresponding to 12-fold symmetry are also studied. The Fourier transform of point masses, placed in vertex positions of the transformed subpatterns, exhibit two-fold, four-fold and six-fold symmetries, although the peaks with highest intensities are situated in rings with apparent octagonal and dodecagonal symmetries.
61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
Issue 29 (22 July 2005)
Received 25 October 2004, in final form 19 April 2005
Published 6 July 2005
Juan García Escudero and Javier García García 2005 J. Phys. A: Math. Gen. 38 6525
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