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# Plant Pattern Formation as a Dynamical System

### Christophe Gole

Smith College

###
January 21, 1999

102 Bradley Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: **
Phyllotactic patterns (from the Greek phyllo (leaf) and taxis
(order)) arise whenever a vascular plant produces at its growing tip
a series of similar botanical elements, such as leaves, scales or
flowerets. The most common and well known of such patterns is one
where the elements are arranged in two families of spirals winding in
opposite directions. The numbers of spirals in each of these families
are, remarkably often, successive numbers in the Fibonacci sequence 1,
1, 2, 3, 5, 8, 13, 21, ... where each term is the sum of the previous
two. This phenomenon, observed for centuries, has not yet received a
satisfactory explanation.

We propose a discrete dynamical system model for plant pattern formation which is compatible with most of the biochemical or biophysical mechanisms that have been conjectured as underlying these patterns. This relatively simple model offers an accessible explaination for the predominence of Fibonacci spiral patterns. It also affords a proof of the dynamical stability of these patterns.

This talk will be accessible to undergraduates.