  Phyllotaxis describes the arrangement of florets, scales or leaves in
composite flowers or plants (daisy, aster, sunflower, pinecone, pineapple). As
a structure, it is a geometrical foam, the most homogeneous and densest
covering of a large disk by Voronoi cells (the florets), constructed by a
simple algorithm: Points placed regularly on a generative spiral constitute a
spiral lattice, and phyllotaxis is the tiling by the Voronoi cells of the
spiral lattice. Locally, neighboring cells are organized as three whorls or
parastichies, labeled with successive Fibonacci numbers. The structure is
encoded as the sequence of the shapes (number of sides) of the successive
Voronoi cells on the generative spiral. We show that sequence and organization
are independent of the position of the initial point on the generative spiral,
that is invariant under disappearance ($T2$) of the first Voronoi cell or,
conversely, under creation of a first cell, that is under growth. This
independence shows how a foam is able to respond to a shear stress, notably
through grain boundaries that are layers of square cells slightly truncated
into heptagons, pentagons and hexagons, meeting at four-corner vertices,
critical points of $T1$ elementary topological transformations.

Soft Condensed Matter;Statistical Mechanics