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: 2013-07-02
Revised: 2014-06-19
Accepted: 2014-06-24
Published online: 2014-09-09
Classification: 92B99,  11H31,  52C15
Keywords: Lattice, hyperbolic geometry, phyllotaxis,sunflower-map
@article{CML_2014__6_1_3_0,
     author = {Roland Bacher},
     title = {On geodesics of phyllotaxis},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {6},
     number = {1},
     year = {2014},
     pages = {3-30},
     language = {en},
     url={cml.centre-mersenne.org/item/CML_2014__6_1_3_0/}
}
Bacher, Roland. On geodesics of phyllotaxis. Confluentes Mathematici, Volume 6 (2014) no. 1, pp. 3-30. https://cml.centre-mersenne.org/item/CML_2014__6_1_3_0/

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