Scott Hotton
Abstract
An important characteristic of plant patterns is the angle between consecutive
organs along the shoot. This is known as the divergence angle and its value is
often nearly constant on an individual plant. This creates a lattice pattern
for the collection of plant organs. When plant shoots are not round the
divergence angles become more variable and the lattice pattern displays crystal
like dislocations.
In this talk I will present a family of dynamical systems which models plant
development. These dynamical systems are based on an inhibitory theory of
plant organ formation and they are able to reproduce the regular and irregular
patterns seen in plants. A constant divergence angle corresponds to a pure
rotation on an attracting invariant circle. The more variable divergence
angles of elliptical systems corresponds to a diffeomorphism on an attractive
invariant circle. It is easy to compare the regular patterns produced by the
model and the regular patterns in plants. I will explain how the theory of
circle maps can be used to make a quantitative comparison between the
irregular patterns of the model and the irregular patterns in actual plants.
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