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.
This is work with Alan Newell.
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