A simple example of a non-Pisot tiling with five-fold symmetry

C. Godrèche , F. Lançon

We consider a tiling of the plane generated by a substitution, the largest eigen-value of which is not a Pisot number. This property leads to unbounded fluctuations of the density in perpendicular space and to the absence of Bragg peaks in the diffraction spectrum of the structure. This spectrum is computed by means of recursion relations between Fourier amplitudes and compared to that of the Penrose tiling.

Domaines: Articles anciens

C. Godrèche, F. Lançon. A simple example of a non-Pisot tiling with five-fold symmetry. Journal de Physique I, 1992, 2 (2), pp.207-220. ⟨10.1051/jp1:1992134⟩. ⟨jpa-00246473⟩