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[2406.00068] Building the Butterfly Fractal: The Eightfold Way

arxiv.org · 152 words · saved by 1 readers

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View PDF HTML (experimental) Abstract:The hierarchical structure of the butterfly fractal -- the Hofstader butterfly, is found to be described by an octonary tree. In this framework of building the butterfly graph, every iteration generates sextuplets of butterflies, each with a tail that is made up of an infinity of butterflies. Identifying {\it butterfly with a tale} as the building block, the tree is constructed with eight generators represented by unimodular matrices with integer coefficients. This Diophantine description provides one to one mapping with the butterfly fractal, encoding…

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