Speaker
Description
In Turing’s study of reaction–diffusion systems, phyllotactic pattern formation was one of his motivations, especially in his later unpublished notes. His work introduced continuous and dynamic approaches to discretely given phyllotactic patterns, inspiring extensive analytical and numerical studies in reaction–diffusion systems. However, Turing himself did not investigate phyllotaxis on surfaces without rotational symmetry or in higher-dimensional spaces.
In our recent work, we propose a unified framework for generating phyllotactic point patterns on general surfaces, Euclidean spaces, and higher-dimensional manifolds with diagonalizable metrics. Our approach relies on algebraic and geometric ideas, including products of linear forms from the geometry of numbers and Lamé systems in orthogonal curvilinear coordinates, offering a complementary perspective to the continuum-based approach by Turing. This framework naturally generalizes the classical golden-angle method to more complex geometries (S. E. Graiff-Zurita & R. OT, 2024; joint work with a student in a 1-year program at Kyushu University). Time permitting, we also discuss the “missing link” between Turing’s reaction–diffusion research and discrete phyllotaxis patterns.