title: Annealing a magnetic cactus into phyllotaxis.
abstract: 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.
authors.affiliation: Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
authors.forename: Cristiano
authors.initials: C
authors.lastname: Nisoli
authors.forename: Nathaniel M
authors.initials: NM
authors.lastname: Gabor
authors.forename: Paul E
authors.initials: PE
authors.lastname: Lammert
authors.forename: J D
authors.initials: JD
authors.lastname: Maynard
authors.forename: Vincent H
authors.initials: VH
authors.lastname: Crespi
mesh_terms: 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*