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Article : Drawing Fibonacci - Colegiul Național din Iași (Iași - Roumanie) Collège Sainte Véronique (Liège)

Résumé de la production: 
Define the Fibonacci word sequence as follows: f_0 = 0, f_1 = 01, f_n = f_(n-1)f_(n-2) (the concatenation of f_(n-1) and f_(n-2)), for n ≥ 2. For example, f_2 = 010, f_3 = 01001, f_4 = 01001010, f_5 = 0100101001001, ... The infinite Fibonacci word is the "limit" of these sequences. Let w_n be the n-th symbol in the infinite Fibonacci word. The Fibonacci curve is a sequence of segments, drawn as follows: - at step 0, draw a segment of length 1 from left to right; - at step n, - if w_n = 0, then draw segment of length 1 in the same direction as the previous segment - if w_n = 1, then draw segment of length 1, turning 90º right if n is even and 90º left if n is odd. Which are the properties of the given curve (e.g.: Does it intersect itself, does it have autosimilarities...). What happens if we change the angle of rotation? What if we change the Fibonacci word with a Sturm word?
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