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 $\varphi_\theta$.
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Submitted on : Friday, May 10, 2013 - 3:32:27 PM
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  • HAL Id : hal-00782907, version 2
  • ARXIV : 1301.7568

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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⟩

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