UNIVERSALITY IN PHYLLOTAXIS: A MECHANICAL THEORY

The following sections are included:

• Introduction

  • The Regularity in Plants

  • Why Fibonacci Numbers?

• Mechanical Theory

  • Growth and Stress

  • Some Historical Remarks

• The Geometric Model

  • Cylindrical Lattices and Parastichies

  • The Space of Cylindrical Lattices

• The Energy Model

  • The Deformation History

  • Symmetries of the Energy

• Universality of Fibonacci Numbers

  • Plan of the Discussion

  • Modular Symmetry and Farey Triangles

  • Farey Partition and the Trajectories of Energy Minima

• Robustness of the Problem

  • Deformation vs. Anisotropic Growth

  • Disk and Cone Geometry

• Summary

• References