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      Annealing a magnetic cactus into phyllotaxis.

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          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.

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          Author and article information

          Journal
          Phys Rev E Stat Nonlin Soft Matter Phys
          Physical review. E, Statistical, nonlinear, and soft matter physics
          American Physical Society (APS)
          1550-2376
          1539-3755
          Apr 2010
          : 81
          : 4 Pt 2
          Affiliations
          [1 ] Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
          Article
          10.1103/PhysRevE.81.046107
          20481786
          e2d16cfa-9eda-4d81-8293-a299cf41dc60
          History

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