On geodesics of phyllotaxis

Abstract : Seeds of sunflowers are often modelled by the map $n\longmapsto \varphi_\theta(n)=\sqrt{n}e^{2i\pi n\theta}$ leading to a roughly uniform repartition with two consecutive seeds separated by the divergence angle $2\pi\theta$ for $\theta$ the golden ratio. We associate to an arbitrary real divergence angle $2\pi \theta$ a geodesic path $\gamma_\theta: \mathbb R_{>0}\longrightarrow \mathrm{PSL}_2(\mathbb Z)\backslash \mathbb H$ of the modular curve and use it for local descriptions of the image $\varphi_\theta(\mathbb N)$ of the phyllotactic map $\varphi_\theta$.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [14 references]

https://hal.archives-ouvertes.fr/hal-00782907
Contributor : Roland Bacher <>
Submitted on : Friday, May 10, 2013 - 3:32:27 PM
Last modification on : Thursday, March 8, 2018 - 9:29:54 AM
Document(s) archivé(s) le : Sunday, August 11, 2013 - 4:08:30 AM

Files

sunflow1.pdf
Files produced by the author(s)

Identifiers

• HAL Id : hal-00782907, version 2
• ARXIV : 1301.7568

Citation

Roland Bacher. On geodesics of phyllotaxis. Confluentes Mathematici, Institut Camille Jordan et Unité de Mathématiques Pures et Appliquées, 2014, 6 (1), pp.3-27. ⟨hal-00782907v2⟩

Record views