submit
english version rss feed
HAL: hal-00367972, version 1

Detailed view  Export this paper
The Fibonacci Word fractal
Alexis Monnerot-Dumaine 1
(2009-02-08)

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.
1:  Indépendant
Aucune
Mathematics/General Mathematics

Mathematics/Dynamical Systems

Mathematics/Combinatorics

Mathematics/Information Theory

Computer Science/Information Theory
Fibonacci word mot fractal fractale curve courbe pattern sturmian combinatorics combinatoire mots
Attached file list to this document: 
PDF
The_Fibonacci_word_fractal.pdf(996.6 KB)

all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...
all articles on CCSd database...