Geodesic
On geodesics of phyllotaxis
Bacher, Roland1
1 Université Grenoble Alpes, Institut Fourier (CNRS UMR 5582), 38000 Grenoble, France
Confluentes Mathematici, Tome 6 (2014) no. 1, pp. 3-30

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Seeds of sunflowers are often modelled by n⟼ϕ 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 :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 .

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DOI : 10.5802/cml.10
Classification : 92B99, 11H31, 52C15
Keywords: Lattice, hyperbolic geometry, phyllotaxis, sunflower-map

Bacher, Roland 1

1 Université Grenoble Alpes, Institut Fourier (CNRS UMR 5582), 38000 Grenoble, France 
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Bacher, Roland. On geodesics of phyllotaxis. Confluentes Mathematici, Tome 6 (2014) no. 1, pp. 3-30. doi: 10.5802/cml.10

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