2025/11/19 by Mosseri, Rémy, Sadoc, Jean-François
Computer Science · Mathematics · Engineering · #Computational Geometry and Mesh Generation #Mathematics and Applications #Structural Analysis and Optimization
paper · doi:10.48550/arxiv.2511.15450
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 ℝ2, the sphere \mathbbS2 and the hyperbolic plane ℍ2). 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 \mathbbS3 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.