Phyllotaxis

Hellwig, Heino; Neukirchner, Thomas

doi:10.1007/s00591-009-0064-8

Cited by 7 publications

(5 citation statements)

References 28 publications

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“…See [13] for a recent survey of the study of phyllotaxis. For the linear model of spiral phyllotaxis, the group action of PSL(2, Z) is described in [14], and the shape convergence of quadrilateral cells is shown in [15]. The circle packing model of spiral phyllotaxis is addressed in [16,17].…”

Section: Corollary 2 (Area Convergence) Suppose That θ/2π Is Badly Ap...mentioning

confidence: 99%

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Area convergence of Voronoi cells on spiral lattices

2021

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Section: Corollary 2 (Area Convergence) Suppose That θ/2π Is Badly Ap...mentioning

confidence: 99%

“…Suppose that μ i,k μ < μ i,k+1 . Then there exist parastichy numbers m, n ∈ {q i , q i,k , q i,k+1 } of Λ μ such that λ μ,n /λ μ,m ∈ D ∪ (−D), (14) where…”

Section: Area Convergence Of Voronoi Cellsmentioning

confidence: 99%

Area convergence of Voronoi cells on spiral lattices

2021

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“…Here we put the fractions in the previous orders in parentheses. The Stern-Brocot tree has been anticipated by Schimper ([21,10]).…”

Section: Appendix a Mediantmentioning

confidence: 99%

“…(B.17) [3,2] : (1, 1), (1,2), (1,3), (3,4), (3,7), (7,10), (10,17), (17,27) [7], the first sequence system [a] is common, the second sequence system [p, a] is rarely observed, and the third sequence system [p − 1, 1, a − 1] is extremely rare. This is consistent with our results in Table 2.…”

Section: Appendix B Continued Fractionmentioning

confidence: 99%

Physical phenomenology of phyllotaxis

Okabe

2011

Journal of Theoretical Biology

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“…In this section, we are going to describe the bifurcation locus for Archimedean Voronoi spiral tilings. See [20,39,40] for the bifurcation diagrams of other spiral tilings.…”

Section: Bifurcation Diagram Of Voronoi Parastichy Pairsmentioning

confidence: 99%

Archimedean Voronoi spiral tilings

Yamagishi

Sushida

2017

J. Phys. A: Math. Theor.

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We study the transition of the number of spirals (called parastichy in the theory of phyllotaxis) within a Voronoi tiling for Archimedean spiral lattices. The transition of local parastichy numbers within a tiling is regarded as a transition at the base site point in a continuous family of tilings. This gives a natural description of the quasiperiodic structure of the grain boundaries. It is proved that the number of tiles in the grain boundaries are denominators of rational approximations of the argument (called the divergence angle) of the generator. The local parastichy numbers are non-decreasing functions of the plastochron parameter. The bifurcation diagram of local parastichy numbers has a Farey tree structure. We also prove Richards’ formula of spiral phyllotaxis in the case of Archimedean Voronoi spiral tilings, and show that, if the divergence angle is a quadratic irrational number, then the shapes of tiles in the grain boundaries are close to rectangles. If the divergence angle is linearly equivalent to the golden section, then the shape of tiles in the grain boundaries is close to square.

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Phyllotaxis

Cited by 7 publications

References 28 publications

Area convergence of Voronoi cells on spiral lattices

Area convergence of Voronoi cells on spiral lattices

Physical phenomenology of phyllotaxis

Archimedean Voronoi spiral tilings

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