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Phyllotaxis: a non-conventional crystalline solution to packing efficiency in situations with radial symmetry

Acta Cryst. (2012). A68, 470-483 (

[Voronoi model] A Voronoi decomposition model.

Topological constraint of circular growth imposes an inflation-deflation invariance taking the place of the classical symmetries of crystallography. It appears in phyllotaxis, the arrangement of florets in composite flowers. 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 florets generated on a Fermat spiral have equal size, but are not all hexagonal. There are annular grains of hexagonal florets (red) separated by grain boundaries [quasiperiodic circular arrays of dislocations (green-blue)].

J.-F. Sadoc, N. Rivier and J. Charvolin