The Fibonacci ruler

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Abstract
The sharp peaks present in the diffraction pattern of a one‐dimensional Fibonacci quasicrystal are explained physically. The explanation rests upon the discovery of periodically positioned spatial regions, with mutually incommensurable spacings, which completely or partially exclude the atoms of the quasicrystal. These sets of periodic exclusion zones act individually as gratings. A ruler‐like optical analog of a 1‐D quasicrystal, in which grating lines replace the hypothetical atoms of the quasicrystal, provides an opportunity to observe quasicrystaldiffraction directly. Such a grating can be produced by hand with simple equipment.

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