[MS12] Mathematical and Computational Perspectives of Phyllotaxis and Growth of Plants

[MS12-02] Voronoi tessellation on Archimedean spiral lattices

*Yoshikazu Yamagishi¹ (1. Ryukoku University (Japan))

Keywords:

spiral lattice,Vororoi tessellation,parastichy,badly approximable

Among the families of spiral lattices defined by a simple formula with constant divergence angle, there are logarithmic and Archimedean spiral lattices. In this talk I will present mathematical properties of Voronoi tessellations on Archimedean spiral lattices. They have grain boundaries, and their parastichies are related to the rational approximations of the divergence angle. If the divergence angle is `badly approximable' like the golden angle, the sequence of the area of the cells is convergent and the limit set of the shape of the quadrilateral cells is a finite set.