Voronoi tiling and circle packing on spiral lattices with rotational symmetry

摘要

Abstract It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices with rotational symmetry is graph-theoretically dual to the bifurcation diagram of Voronoi tessellations, by using the relative metric. If the rotation parameter (called divergence angle) is badly approximable, then the aspect ratio of the quadrilateral Voronoi cells is bounded. If the divergence angle is linearly equivalent to the golden section, then the shape of the quadrilateral cells tend to square as the plastochron ratio tends to 1.