Narrow Results

Phyllotaxis of plant organs, bacterial ordering and animal coat patterns are analyzed for homogeneity and density. The patterns are approximated by 15 tiles and characterized by the self-coordination numbers T₁, T₂, T₃ of the nearest, next-nearest and third neighbors of the vertices of the tiles. Homogeneous structures with integer T_i values and maximum densities are obtained for distichous, whorled or spiral growth of leaves. Similar T₁ values, such as T₁=5 and 6 of sunflower seeds or bacteriae, give rise to maximum density. Inhomogeneous structures like the striped patterns of zebras with T₁=1, 2 and 3 connections have a higher density than homogeneous stripes with T₁=2. Maximum density is also obtained in icosahedral viruses.