  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.
