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COMPLEXITY OF THE FIBONACCI SNOWFLAKE

Laboratoire d'informatique Formelle, Université du Québec à Chicoutimi, 555, boul. de l'Université, Chicoutimi, (QC) Canada G7H 2B1, Canada

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SREČKO BRLEK

Laboratorie de Combinatoire et d'informatique Mathématique (LaCIM), Université du Québec à Montréal, C. P. 8888, Succ. Centre-ville, Montréal (QC) Canada H3C 3P8, Canada

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SÉBASTIEN LABBÉ

Laboratorie de Combinatoire et d'informatique Mathématique (LaCIM), Université du Québec à Montréal, C. P. 8888, Succ. Centre-ville, Montréal (QC) Canada H3C 3P8, Canada

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MICHEL MENDÈS FRANCE

Département de Mathématiques, UMR 5251, Université Bordeaux 1, 351 Cours de la Libération, F-33405 Talence Cedex, France

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https://doi.org/10.1142/S0218348X12500235Cited by:3 (Source: Crossref)

Abstract

The object under study is a particular closed and simple curve on the square lattice ℤ² related with the Fibonacci sequence F_n. It belongs to a class of curves whose length is 4F_3n+1, and whose interiors tile the plane by translation. The limit object, when conveniently normalized, is a fractal line for which we compute first the fractal dimension, and then give a complexity measure.

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