in The European Physical Journal E, 39(1), 1-11; DOI 10.1140/epje/i2016-16007-8
author:
- Nicolas Rivier
- 'Jean-François Sadoc'
- Jean Charvolin
title: 'Phyllotaxis: a framework for foam topological evolution'
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Introduction
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A foam can be represented as a space-filling cellular network, a tessellation, usually random. In 3D, the cells are bounded by interfaces connected three by three on edges that meet four by four on vertices. In 2D, the cells are bounded by edges that meet three by three on vertices. This generic description holds unless the meeting point has been especially adjusted. The foam has a topological dual in which a vertex is associated with each cell and an edge joining two vertices traverses the interface between two cells. Generically, the cells in the dual are simplices, triangles in 2D and tetrahedra in 3D. It is often assumed that the elements of the foam are physical elements, i.e the cells are closed bubbles filled by a discontinuous gas phase and the space between them (the interface) is filled by the continuous liquid phase. Edges and vertices, called Plateau borders are distinct in dry foams [@weaire]. In phyllotaxis, the interfaces between florets are not physical entities. Nevertheless, topological defects such 