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Figure 1
The one-dimensional Fibonacci sequence in the two-dimensional description. (a) The quasiperiodic sequence …LSLSLL… [L (S) means long (short) interval] results from the cut of the two-dimensional hypercrystal structure by the physical space, V||. The two-dimensional lattice is decorated with line segments (atomic surfaces or occupation domains) parallel to the perpendicular space, [V^\perp]. (b) A one-dimensional periodic average structure can be obtained by oblique projection of the two-dimensional structure along the grey stripes. (c) The one-dimensional diffraction pattern results from the projection of the two-dimensional one onto physical space. The intensities, [I({H^ \bot } )], of the Bragg reflections decrease with the function [({{{\sin H^ \bot } / {H^ \bot }}} ){}^2] drawn on the right. The reflections related to the periodic average structure are connected by the red line perpendicular to the projection direction in (b).

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ISSN: 2053-2733
Volume 64| Part 1| January 2008| Pages 1-11
https://doi.org/10.1107/S0108767307038627
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