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- Q5446404 subject Q5463728.
- Q5446404 subject Q7464146.
- Q5446404 abstract "A Fibonacci crystal or quasicrystal is a model used to study systems with aperiodic structure. Both names are acceptable as a 'Fibonacci crystal' denotes a quasicrystal and a 'Fibonacci' quasicrystal is a specific type of quasicrystal. Fibonacci 'chains' or 'lattices' are other synonyms used with regard to the dimensionality of the model. While it is used mostly as a theoretical construct, physical models are also implemented for empirical checks. Most of its applications pertain to various areas of solid state physics. The mathematical properties of the Fibonacci word and related topics are well researched and readily applied in such studies. The elements of a Fibonacci crystal structure are arranged in one or more spatial dimensions according to the sequence given by the Fibonacci word. The Fourier transform of such arrangements consists of discrete values, which is the defining property for crystals. In an algebraic form the sequence is expressed with a matrix whose eigenvalues are Pisot numbers. This feature guarantees that its Fourier transform is discrete. Material waves with appropriate length would interfere constructively when interacting with a Fibonacci structured physical system. For instance, when submitted to X-rays, a Fibonacci quasicrystal would produce Bragg peaks. Other features describing media behaviour such as damping, transmitivity, etc. can be evidenced on Fibonacci models.The Fibonacci-based constructions are an obvious example of quasicrystals that do not possess a 'forbidden symmetry'. Their diffraction pattern would be of a square type with the intensities arranged in a fractal pattern.".
- Q5446404 thumbnail Binary_Fibonacci_tiling.svg?width=300.
- Q5446404 wikiPageWikiLink Q1030382.
- Q5446404 wikiPageWikiLink Q263214.
- Q5446404 wikiPageWikiLink Q34777.
- Q5446404 wikiPageWikiLink Q43533.
- Q5446404 wikiPageWikiLink Q5463728.
- Q5446404 wikiPageWikiLink Q6520159.
- Q5446404 wikiPageWikiLink Q715396.
- Q5446404 wikiPageWikiLink Q7464146.
- Q5446404 wikiPageWikiLink Q749729.
- Q5446404 wikiPageWikiLink Q897227.
- Q5446404 comment "A Fibonacci crystal or quasicrystal is a model used to study systems with aperiodic structure. Both names are acceptable as a 'Fibonacci crystal' denotes a quasicrystal and a 'Fibonacci' quasicrystal is a specific type of quasicrystal. Fibonacci 'chains' or 'lattices' are other synonyms used with regard to the dimensionality of the model. While it is used mostly as a theoretical construct, physical models are also implemented for empirical checks.".
- Q5446404 label "Fibonacci quasicrystal".
- Q5446404 depiction Binary_Fibonacci_tiling.svg.