Do plants know math?

• Position: Horticulture

For more than three centuries, botanists and mathematicians have marveled at the complex and beautiful spiral patterns that form as plants develop. As they generate leaves around a stem, or seeds or flowers in a blossom, plants as diverse as broccoli, pinecones, artichokes, and water lilies create intricate spirals that follow a well-known mathematical sequence of numbers.

"A prominent theme in science today, whether in biology, math, or computer science, is the generation of complex patterns through simple rules," explains Chris Gole, professor of mathematics, Smith College, Northampton, Mass. "Plants have been succeeding at this throughout their evolution, with great consistency and visual beauty."

To highlight the mathematical underpinnings of phyllotaxis, which refers to the arrangement of leaves or other botanical elements around a stem, Gole and Pau Atela, associate professor of mathematics, teamed up with Michael Marcotrigiano and Madelaine Zadik of the Smith College Botanic Garden to produce an exhibition, "Plant Spirals: Beauty You Can Count On" (www.math.smith.edu/phyllo/expo), that depicts with rare beauty and clarity the geometry and biology of plant spiral formation.

Through a computer animation, scanning electron micrographs, and large-scale panels featuring vivid color images and historical contexts, the viewer is guided from the natural phenomena to a recently developed simple mathematical model that reproduces the spiral patterns seen in plants. The model is based on a branch of mathematics known as dynamical systems, which includes chaos theory.

Gole notes that plant spirals often form according to the Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13 ...), in which each digit is the sum of the previous two. The...