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| HAL: hal-00367972, version 1 |
| Detailed view |  Export this paper |
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| The Fibonacci Word fractal |
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| Alexis Monnerot-Dumaine 1 |
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| (2009-02-08) |
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| 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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| 1: | Indépendant |
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Aucune |
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| Subject | : | Mathematics/General Mathematics Mathematics/Dynamical Systems Mathematics/Combinatorics Mathematics/Information Theory Computer Science/Information Theory and Coding |
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| Fibonacci word mot fractal fractale curve courbe pattern sturmian combinatorics combinatoire mots |
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| Attached file list to this document: | |||||
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| hal-00367972, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00367972 | |
| oai:hal.archives-ouvertes.fr:hal-00367972 | |
| From: Alexis Monnerot-Dumaine | |
| Submitted on: Friday, 13 March 2009 10:36:14 | |
| Updated on: Sunday, 5 April 2009 12:47:30 | |
