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

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

doi:10.1107/S0108767312018910

Figure 9
First-neighbour distances between sites s and $[s+\delta s]$ . Blue for the interval $[\delta s]$ equal to the smaller positive Fibonacci number in the list of Table 1

; green for the next interval; red for the third positive interval; and purple for the last one (occurring only if the Voronoi cell is a heptagon). Thus green, blue and red correspond to distance along the three visible parastichies. Each continuous curve corresponds to a given Fibonacci number that appears in different annuli. For instance, f₁₁ = 89 appears between s = 290 and 5926 leading to a continuous curve which is successively purple, red, green and blue. Each lower crossing of two curves corresponds to a grain boundary, the upper crossing is in the middle of a hexagonal ring. The scaling parameter in equation (1)

is a = 1, so the distances are approximately in the range [1.676, 2.506] with a mean value 1.903.