Annealing a magnetic cactus into phyllotaxis.
The appearance of mathematical regularities in the disposition of leaves on a stem, scales on a pine-cone, and spines on a cactus has puzzled scholars for millennia; similar so-called phyllotactic patterns are seen in self-organized growth, polypeptides, convection, magnetic flux lattices and ion beams. Levitov showed that a cylindrical lattice of repulsive particles can reproduce phyllotaxis under the (unproved) assumption that minimum of energy would be achieved by two-dimensional Bravais lattices. Here we provide experimental and numerical evidence that the Phyllotactic lattice is actually a ground state. When mechanically annealed, our experimental "magnetic cactus" precisely reproduces botanical phyllotaxis, along with domain boundaries (called transitions in Botany) between different phyllotactic patterns. We employ a structural genetic algorithm to explore the more general axially unconstrained case, which reveals multijugate (multiple spirals) as well as monojugate (single-spiral) phyllotaxis.
Nisoli
Cristiano
C
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Gabor
Nathaniel M
NM
Lammert
Paul E
PE
Maynard
J D
JD
Crespi
Vincent H
VH
D000465:Algorithms; D032701:Biomimetics / Q000379:methods*; D029421:Cactaceae / Q000033:anatomy & histology*; D005823:Genetics; D008280:Magnetics; D018515:Plant Leaves / Q000033:anatomy & histology*; D018547:Plant Stems / Q000033:anatomy & histology*