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In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of modern scientific data visualization. The name reflects the fact that, as Hofstadter wrote, "the large gaps [in the graph] form a very striking pattern somewhat resembling a butterfly."

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  • Mariposa de Hofstadter (es)
  • Hofstadter's butterfly (en)
  • Farfalla di Hofstadter (it)
  • ホフスタッターの蝶 (ja)
  • Бабочка Хофштадтера (ru)
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  • En física de la materia condensada, la mariposa de Hofstadter se refiere a las propiedades del espectro de energía de electrones en una red cristalina en presencia de un campo magnético. La figura, que presenta autosimilitud y comportamiento fractal, fue descubierta por Douglas Hofstadter en 1976.​ La mariposa de Hofstadter jugó un rol histórico esencial en la teoría del efecto Hall cuántico y de la topología cuántica. (es)
  • La Farfalla di Hofstadter è un frattale scoperto da Douglas Hofstadter, che lo descrisse nel 1976 su un articolo sui livelli energetici degli elettroni di Bloch nei campi magnetici.Dà una rappresentazione grafica dello spettro del per a diverse frequenze, che si rivelò per visualizzare un'ovvia auto Auto similarità.È uno dei rari frattali scoperti in fisica, insieme al teorema di Kolmogorov-Arnold-Moser. Nel 2013 viene trovata la struttura a Farfalla di Hofstadter nel grafene da due gruppi di ricerca indipendenti, uno dell'Università di Manchester e l'altro del City College di New York. (it)
  • In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of modern scientific data visualization. The name reflects the fact that, as Hofstadter wrote, "the large gaps [in the graph] form a very striking pattern somewhat resembling a butterfly." (en)
  • Бабочка Хофштадтера — фрактальная структура, открытая Дугласом Хофштадтером и описанная им в 1976 году в статье, посвящённой уровням энергии блоховских электронов в магнитном поле. Графическое представление спектра почти оператора Матье (англ. Almost Mathieu operator) при λ = 1 на разных частотах обладает самоподобием. Таким образом, это одна из редких фрактальных структур, обнаруженных в физике. Математическое описание спектра было частично разработано М. Я. Азбелем в 1964 году (модель Азбеля-Хофштадтера), и полностью описано и графически представлено в виде геометрической структуры Д. Хофштадтером в 1976 году. (ru)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/2017-09-22-113215_627x350_scrot.png
  • http://commons.wikimedia.org/wiki/Special:FilePath/Gplot_by_Hofstadter.jpg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Hofstadter's_butterfly_monochrome_with_axes_en.jpg
  • http://commons.wikimedia.org/wiki/Special:FilePath/Img_8960x5600.png
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