Hausdorff Dimension of Generalized Fibonacci Word Fractals

preprint2016arXivOpen access

Abstract

Fibonacci word fractals are a class of fractals that have been studied recently, though the word they are generated from is more widely studied in combinatorics. The Fibonacci word can be used to draw a curve which possesses self-similarities determined by the recursive structure of the word. The Hausdorff dimension of the scaling limit of the finite Fibonacci word curves is computed for ii-Fibonacci curves and any drawing angle between 00 and π/2π/2.

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