January 20, 2003
DO PLANTS KNOW MATH?
Innovative Exhibition and
Web Site Offer Explanation for the Stunningly Intricate Spiral
Patterns Found in Common Flowers and Vegetables
FOR IMMEDIATE RELEASE
Editor's note: High-res images
(300 dpi) of plant spirals from the exhibition are available.
To select, see http://www.math.smith.edu/phyllo/expo
and contact Laurie Fenlason with requests [email@example.com].
NORTHAMPTON, Mass.-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 Smith College Associate
Professor of Mathematics Chris Golé.
"Plants have been succeeding at this throughout their evolution,
with great consistency and visual beauty," he adds.
To highlight the mathematical underpinnings of phyllotaxis, which
refers to the arrangement of leaves or other botanical elements
around a stem, Golé and his Smith colleague Pau Atela,
associate professor of mathematics, teamed up with Michael Marcotrigiano
and Madelaine Zadik of the Smith College Botanic Garden to produce
an unusual exhibition. "Plant Spirals: Beauty You Can Count
On" is an exhibition [Web site at www.math.smith.edu/phyllo/expo]
accessible to a general audience, 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
Golé 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 spiral helixes visible
in plants usually come in two sets winding in opposite directions.
The numbers of spirals are most often two consecutive Fibonacci
numbers. The flower of an English daisy, pictured in the exhibition,
consists of 21 spirals clockwise and 34 counter-clockwise. A
pinecone pictured has eight spirals in one direction and 13 in
the other, eight and 13 being successors in the Fibonacci sequence.
To understand why Fibonacci numbers predominate in plant spirals,
Golé and Atela started with the theories of 19th-century
botanist Wilhelm Hofmeister, who observed that a plant's leaves
emerge at the least crowded spot around a circular meristem or
growing tip. They are then radially displaced from the center.
The dynamical systems model developed by Atela, Golé and
Scott Hotton of Miami University, based on the recent work of
French physicists Stéphane Douady and Yves Couder, suggests
that those simple geometric rules are enough to produce the spiral
patterns with Golden Angle and Fibonnaci numbers that appear
"Whether plants 'know' mathematics or not," Atela remarks,
"they are clearly programmed to follow a common set of developmental
rules, which would suggest that these patterns confer evolutionary
"That the intricate patterns in nature, such as a leaf arrangement,
leopard spots and butterfly wings, may all be regulated by simple
and related mechanisms is an intriguing concept," Marcotrigiano
"Plant Spirals" is the debut show in the Church Exhibition
Gallery of the Botanic Garden's Lyman Plant House. The exhibition
is free and open to the public and will be on view through March
31. The gallery is open daily from 8:30 a.m. to 4:30 p.m. and
is wheelchair accessible. The greenhouses are currently closed
for renovation. Areas beyond the Church Gallery will reopen to
the public on March 1.
The entire campus of Smith College was originally planned and
planted 100 years ago as a botanic garden and arboretum, designed
by the landscape architecture firm of Frederick Law Olmsted.
The Botanic Garden encompasses the 125 contiguous acres of the
campus; the Lyman Conservatory, with 12,000 square feet under
glass; and a variety of specialty gardens. The garden is open
to the public and contains more than 7,000 labeled and mapped
plants. Adjacent to the Lyman Conservatory are the rock garden,
one of the oldest in America, and the systematics garden, in
which plants are arranged by family. Other gardens around the
campus include a Japanese viewing pavilion, a wildflower and
woodland garden, an herb garden, a terraced rose garden and a
formal knot and gazebo garden.
Smith College is consistently ranked among the nation's foremost
liberal arts colleges. Enrolling 2,800 students from every state
and 55 other countries, Smith is the largest undergraduate women's
college in the country.
-- 30 --