Phyllotactic Patterns on Plants
by
Patrick Shipman
University of Arizona
Coauthors: Alan Newell

We show how phyllotaxis (the arrangement of leaves on plants) and the deformation configurations seen on plant surfaces can be understood as the preferred nonlinear buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is the recognition that the optimal configuration is one which essentially minimizes the strain energy as measured by the product of the Airy stress and Gaussian curvature of the deformed plant surface. The cubic nonlinear component of this contribution is largest negative on configurations that are triads of almost periodic deformations whose local wavevectors add to zero. Based on this simple observation, we can reproduce a wide spectrum of plant patterns and show how the occurances of Fibonacci-like sequences and the golden angle are natural consequences. We also study roll-hexagon competition and defects on plants.

Date received: October 14, 2003