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| HAL : hal-00367972, version 1 |
| Fiche détaillée |  Récupérer au format |
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| The Fibonacci Word fractal |
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| Alexis Monnerot-Dumaine 1 |
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| (08/02/2009) |
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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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| Domaine | : | Mathématiques/Mathématiques générales Mathématiques/Systèmes dynamiques Mathématiques/Combinatoire Mathématiques/Théorie de l'information et codage Informatique/Théorie de l'information et codage |
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| Fibonacci word mot fractal fractale curve courbe pattern sturmian combinatorics combinatoire mots |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00367972, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00367972 | |
| oai:hal.archives-ouvertes.fr:hal-00367972 | |
| Contributeur : Alexis Monnerot-Dumaine | |
| Soumis le : Vendredi 13 Mars 2009, 10:36:14 | |
| Dernière modification le : Dimanche 5 Avril 2009, 12:47:30 | |
