Presentation Information
[MS12-01]Pattern formation on general surfaces and 3D volumes via a generalization of the golden angle method
*Ryoko Oishi-Tomiyasu1 (1. Kyushu University (Japan))
Keywords:
phyllotaxis,pattern formation,generalized golden angle method,curved surface,3D
Spiral phyllotaxis patterns are widely observed in plants and emerge through developmental processes that optimize packing efficiency. These patterns can also be generated numerically using the golden angle method. We extend this method to general surfaces and 3D manifolds, providing a mathematical framework for this biological pattern formation [1]. From a mathematical perspective, our method offers a new systematic construction of nearly uniform point packings on arbitrary Riemannian manifolds with a locally diagonalizable metric, including Euclidean spaces of any dimension.
This extension of the classical golden angle method provides mathematical insights into phyllotaxis patterns and related biological packing phenomena. The proposed method has a much broader parameter space than conventionally assumed for the classical golden angle method, making it widely applicable for modeling plant morphology and the patterns observed on plant surfaces. Investigating the plant morphospace in the parameter space and its biological implications could provide valuable insights into the evolutionary development of plant morphology.
Phyllotaxis patterns in flowerheads without circular symmetry have been examined under the Hofmeister hypothesis in [2]. Recent studies [3,4] have also explored L-systems and Turing patterns on curved surfaces and in 3D volumes. Establishing connections between these frameworks and the generalized golden angle method is an important direction for future research.
[1] E. Graiff Zurita & R. Oishi-Tomiyasu, “Packing Theory Derived from Phyllotaxis and Products of Linear Forms”, Constructive Approximation 60, pp. 515–545, 2024.
[2] Prusinkiewicz, et. al., “Phyllotaxis without symmetry: what can we learn from flower Journal of Experimental Botany”, FLOWERING NEWSLETTER REVIEW 73(11) pp. 3319–3329, 2022.
[3] Godin & F. Boudon, “Riemannian L-systems: Modeling growing forms in curved spaces”, https://arxiv.org/abs/2404.03270, 2024.
[4] D. Rueda-Contreras et. al., “Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis”, PLoS ONE 13(8): e0201746, 2018.
This extension of the classical golden angle method provides mathematical insights into phyllotaxis patterns and related biological packing phenomena. The proposed method has a much broader parameter space than conventionally assumed for the classical golden angle method, making it widely applicable for modeling plant morphology and the patterns observed on plant surfaces. Investigating the plant morphospace in the parameter space and its biological implications could provide valuable insights into the evolutionary development of plant morphology.
Phyllotaxis patterns in flowerheads without circular symmetry have been examined under the Hofmeister hypothesis in [2]. Recent studies [3,4] have also explored L-systems and Turing patterns on curved surfaces and in 3D volumes. Establishing connections between these frameworks and the generalized golden angle method is an important direction for future research.
[1] E. Graiff Zurita & R. Oishi-Tomiyasu, “Packing Theory Derived from Phyllotaxis and Products of Linear Forms”, Constructive Approximation 60, pp. 515–545, 2024.
[2] Prusinkiewicz, et. al., “Phyllotaxis without symmetry: what can we learn from flower Journal of Experimental Botany”, FLOWERING NEWSLETTER REVIEW 73(11) pp. 3319–3329, 2022.
[3] Godin & F. Boudon, “Riemannian L-systems: Modeling growing forms in curved spaces”, https://arxiv.org/abs/2404.03270, 2024.
[4] D. Rueda-Contreras et. al., “Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis”, PLoS ONE 13(8): e0201746, 2018.