Like a crystal, it is based on a lattice, but it is a spiral lattice, and the structure is encoded as a one-dimensional sequence of all the cells in the pattern. Like any foam, phyllotaxis is structured into layers [@oguey; @AsBoRi].

The tiling of phyllotaxis
=========================

A spiral lattice
----------------

Phyllotaxis describes the arrangement of florets, scales or leaves in composite flowers or plants (daisy, aster, sunflower, pine cone, pineapple). Geometrically, it is a foam (albeit ordered and organized), the most homogeneous and densest covering of a large disk by Voronoi cells (the florets) [@ridley]. The Voronoi cell (or Dirichlet domain) associated with a point is defined as the region of space nearer to it than to any other point in the set. Points placed regularly on a generative spiral constitute a spiral lattice, and phyllotaxis is the tiling by the Voronoi cells of the spiral lattice. The number of points on the generative spiral increases as the flower grows.

First, one constructs on a surface of constant Gauss curvature (plane, sphere, cone, cylinder) a spiral lattice defined by a parametric equation (with a parameter $s$) for a generative spiral. Discrete points, dual of cells, are set regularly at integer 