Phyllotaxis or the properties of spiral lattices. - II. Packing of circles along logarithmic spirals

F. Rothen , A.-J. Koch

Phyllotaxis can be identified with the study of spiral lattices which are useful as models for many botanical structures (arrangements of the inner florets of a daisy, of the scales of a pineapple...). We consider a geometrical idealization of such networks : a lattice of tangent circles aligned along a logarithmic spiral. using conditions for close-packing of such circles, we show that the parastichy numbers belong to a generalized Fibonacci sequence. Moreover, if « regular » parastichy transitions only occur in the lattice, the divergence tends to a noble number. On the contrary a rational number is reached after an infinite sequence of singular transitions.

Mots clés: lattice theory and statistics

Domaines: Articles anciens

F. Rothen, A.-J. Koch. Phyllotaxis or the properties of spiral lattices. - II. Packing of circles along logarithmic spirals. Journal de Physique, 1989, 50 (13), pp.1603-1621. ⟨10.1051/jphys:0198900500130160300⟩. ⟨jpa-00211020⟩