Energetic Approach to Phyllotaxis

@article{Levitov1991EnergeticAT,
  title={Energetic Approach to Phyllotaxis},
  author={L. S. Levitov},
  journal={EPL (Europhysics Letters)},
  year={1991},
  volume={14},
  pages={533 - 539}
}
Soft lattices subjected to strong compression are studied. Their equilibrium states form a hierarchical system of quasi-bifurcations. Underlying SL(2, Z) ⊗ Z2 symmetry of the problem is revealed. The deterministic “principle” of maximal denominator for quasi-bifurcations is proven analytically, thus explaining the universality of the appearance of Fibonacci numbers for dynamically accessible lattices. The symmetry provides the relation between the hierarchical structure and the Cayley tree with… 

References

Phyllotaxis of flux lattices in layered superconductors.

  • Levitov
  • Physics
    Physical review letters
  • 1991
It is shown that dynamically accessible lattices are characterized by pairs of consecutive Fibonacci numbers.