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Preprints, Working Papers, ... Year : 2009

The Fibonacci Word fractal

Abstract

The Fibonacci Word Fractal is a self-similar fractal curve based on the Fibonacci word through a simple and interesting drawing rule. This fractal reveals three types of patterns and a great number of self-similarities. We show a strong link with the Fibonacci numbers, prove several properties and conjecture others, we calculate its Hausdorff Dimension. Among various modes of construction, we define a word over a 3-letter alphabet that can generate a whole family of curves converging to the Fibonacci Word Fractal. We investigate the sturmian words that produce variants of such a pattern. We describe an interesting dynamical process that, also, creates that pattern. Finally, we generalize to any angle.
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Dates and versions

hal-00367972 , version 1 (13-03-2009)

Identifiers

  • HAL Id : hal-00367972 , version 1

Cite

Alexis Monnerot-Dumaine. The Fibonacci Word fractal. 2009. ⟨hal-00367972⟩

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