On geodesics of phyllotaxis

Roland Bacher

doi:10.5802/cml.10

Roland Bacher ¹

¹ Université Grenoble Alpes, Institut Fourier (CNRS UMR 5582), 38000 Grenoble, France

Confluentes Mathematici, Tome 6 (2014) no. 1, pp. 3-27.

Résumé

Seeds of sunflowers are often modelled by $n ⟼ ϕ_{θ} (n) = \sqrt{n} e^{2 i π n θ}$ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance $2 π θ$ for $θ$ the golden ratio. We associate to such a map $ϕ_{θ}$ a geodesic path $γ_{θ} : ℝ_{> 0} ⟶ {PSL}_{2} (ℤ) ∖ ℍ$ of the modular curve and use it for local descriptions of the image $ϕ_{θ} (ℕ)$ of the phyllotactic map $ϕ_{θ}$ .

DOI : 10.5802/cml.10

Classification : 92B99, 11H31, 52C15
Mots clés : Lattice, hyperbolic geometry, phyllotaxis, sunflower-map

Affiliations des auteurs :

Roland Bacher ¹

¹ Université Grenoble Alpes, Institut Fourier (CNRS UMR 5582), 38000 Grenoble, France

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Roland Bacher. On geodesics of phyllotaxis. Confluentes Mathematici, Tome 6 (2014) no. 1, pp. 3-27. doi : 10.5802/cml.10. https://cml.centre-mersenne.org/articles/10.5802/cml.10/

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