spiral, the boundary remains close to circular. This optimal compactness explains why we have used phyllotaxis as a model for a 2D foam confined inside a circular boundary [@sadoc1]. The phyllotactic structure is also hyperuniform [@torquato] : although ordered, it is under steady strain through growth, but remains invariant under the elementary, local topological transformations ($T1$ and $T2$) that the strain induces.)

The phyllotactic pattern of a set of 3000 points on a plane with their Voronoi cells is shown in figure \[fg2\]. The structure is defined by the generative spiral which is not visible: the cells corresponding to successive points $s = 0,1,2,...,n$ on the generative spiral are not neighbors. But the pattern does exhibit visible spirals of nearest neighbor cells. Through every hexagonal cell there are three such spirals, called by botanists “parastichies”: The neighbors [^2] to cell $s$ are $s\pm f_{i-1},s\pm f_{i-2},s\pm f_{i-3}$. The parastichies split up or merge on the non-hexagonal cells which are concentrated on thin rings of defects. On the defect rings, the two parastichies that continue from one grain to the next are orthogonal and the cells are truncated rectangles [@rivier3]. The defects are pentagon-heptagon dipoles acting as dislocations, gathered into grain boundaries. 