On geodesics of phyllotaxis
Confluentes Mathematici, Volume 6 (2014) no. 1, pp. 3-30.

Seeds of sunflowers are often modelled by nϕ θ (n)=ne 2iπnθ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance 2πθ for θ the golden ratio. We associate to such a map ϕ θ a geodesic path γ θ : >0 PSL 2 () of the modular curve and use it for local descriptions of the image ϕ θ () of the phyllotactic map ϕ θ .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/cml.10
Classification: 92B99,  11H31,  52C15
Keywords: Lattice, hyperbolic geometry, phyllotaxis,sunflower-map
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, Volume 6 (2014) no. 1, pp. 3-30. doi : 10.5802/cml.10. https://cml.centre-mersenne.org/articles/10.5802/cml.10/

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