title: Phyllotaxis: a framework for foam topological evolution.
abstract: 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, labelled 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.
authors.affiliation: Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg, F-67084, Strasbourg, France. rivier@ipcms.unistra.fr.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Rivier
authors.affiliation: Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, Université de Paris-Sud, F-91405, Orsay, France.
authors.forename: Jean-François
authors.initials: JF
authors.lastname: Sadoc
authors.affiliation: Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, Université de Paris-Sud, F-91405, Orsay, France.
authors.forename: Jean
authors.initials: J
authors.lastname: Charvolin
mesh_terms: D000465:Algorithms; D048430:Cell Shape; D035264:Flowers / Q000166:cytology; D019684:Magnoliopsida / Q000166:cytology* / Q000254:growth & development; D008962:Models, Theoretical; D018515:Plant Leaves / Q000166:cytology
keywords: Flowing Matter: Liquids and Complex Fluids
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012302
references.pmid: 25679618
references.citation: Biophys J. 1997 Jul;73(1):38-44
references.pmid: 9199769
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Jun;53(6):6181-6191
references.pmid: 9964980