Annealing a Magnetic Cactus into Phyllotaxis

TL;DR

This study demonstrates that a magnetic lattice can be mechanically annealed to naturally form phyllotactic patterns, providing experimental and numerical evidence that these arrangements are ground states of repulsive particle systems.

Contribution

The paper provides the first experimental validation that phyllotactic patterns are ground states of repulsive lattices, using a magnetic cactus model and genetic algorithms to explore pattern diversity.

Findings

Magnetic cactus reproduces botanical phyllotaxis upon annealing.

Phyllotactic patterns are confirmed as ground states of the system.

Discovery of multijugate and monojugate phyllotaxis through computational exploration.

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.