Some attempts toward 3-dimensional Phyllotaxy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908665593724928 |
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| author | Mosseri, Rémy Sadoc, Jean-François |
| author_facet | Mosseri, Rémy Sadoc, Jean-François |
| contents | This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known contructions for these sets on $2D$ manifolds of constant curvature (the Euclidean plane $\mathbb{R}^2$, the sphere $\mathbb{S}^2$ and the hyperbolic plane $\mathbb{H}^2$). We then propose a first attempt to get a $3D$ phyllotactic set by piling up suitably shifted Euclidean $2D$ phyllotactic sets. A different, radially triggered, solution is then analyzed. An interesting phyllotactic set on the hypersphere $\mathbb{S}^3$ is then generated using a Hopf fibration approach. Finally,a simple 4-dimensional example is presented, generated as a simple product of two 2-dimensional planar sets. A $3D$ phyllotaxy candidate is then derived by applying a "Cut and Project" algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some attempts toward 3-dimensional Phyllotaxy Mosseri, Rémy Sadoc, Jean-François Other Condensed Matter This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known contructions for these sets on $2D$ manifolds of constant curvature (the Euclidean plane $\mathbb{R}^2$, the sphere $\mathbb{S}^2$ and the hyperbolic plane $\mathbb{H}^2$). We then propose a first attempt to get a $3D$ phyllotactic set by piling up suitably shifted Euclidean $2D$ phyllotactic sets. A different, radially triggered, solution is then analyzed. An interesting phyllotactic set on the hypersphere $\mathbb{S}^3$ is then generated using a Hopf fibration approach. Finally,a simple 4-dimensional example is presented, generated as a simple product of two 2-dimensional planar sets. A $3D$ phyllotaxy candidate is then derived by applying a "Cut and Project" algorithm. |
| title | Some attempts toward 3-dimensional Phyllotaxy |
| topic | Other Condensed Matter |
| url | https://arxiv.org/abs/2511.15450 |