Phyllotaxis as a Dynamical System

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Phyllotaxis as a Dynamical System
The crystal-like symmetries found in many
biological structures reflect the simple
geometrical constraints imposed by the close
packing of equivalent subunits. Phyllotaxis, i.e.
the leaf and flower patterns observed in plants,
is a particularly striking problem because the
patterning process reaches beyond the simple
steric interactions that are commonly used to
explain the symmetries of inorganic and organic
crystals. The goal of this project is to
determine empirically and formally why some
phyllotactic configurations are more common than
others in plants. Our experimental
observations and numerical computations have
shown that the typical phyllotactic patterns
require a specific set of initial conditions to
be expressed. We have developed a close-packing
model which can reproduce patterns such as the
one illustrated here with greater accuracy than
the classical models based on spiral lattices.
We are currently analyzing the space of patterns
that can be generated with this model. The
mathematical simplicity of the model will allow
us to determine formally the set of conditions
required to achieve specific patterns.
Phyllotactic pattern in an artichoke. Here
flower primordia are packed onto the apex of the
plant and form a characteristic pattern. Green
lines highlight the sequence of contacts that led
to the final pattern.
J. Dumais, Harvard University Work performed at
Center for Nanoscale Systems -Harvard