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 2-D 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.

9 Pages 11 Figures

References in corpus (2)

• Static and Dynamical Phyllotaxis in a Magnetic Cactus
• Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond

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• Plastic deformation of tubular crystals by dislocation glide
• Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder
• Shape multistability in flexible tubular crystals through interactions of mobile dislocations