From: Spudboy100@aol.com
Date: Sun Apr 06 2003 - 00:48:15 MST
<A HREF="http://www.nature.com/nsu/030331/030331-3.html">http://www.nature.com/nsu/030331/030331-3.html>
W.W. W. D. = What Would Wolfran Do?
Is it a starfish? Is it an orchid? No, it's Superformula.
For centuries scientists have sought to express natural forms in mathematical
One simple equation can generate a vast diversity of natural shapes, a
"When I found the formula, all these beautiful shapes came rolling out of my
The Superformula is a modified version of the equation for a circle1.
Varying both proportion and symmetry together produces shapes with any number
For centuries, scientists have sought to express natural forms - such as the
"Describing form is one of the more intractable problems in biology," says
The Superformula might provide a single, simple framework for analysing and
The Superformula produces regular and irregular shapes with any number of
What's less clear is whether nature uses the formula to generate different
Other, more complicated, single equations can produce a similar diversity of
Gielis acknowledges that the formula describes nature's end product, not how
Gielis, J. A generic geometric transformation that unifies a wide range of
© Nature News Service / Macmillan Magazines Ltd 2003
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: Sun Apr 06 2003 - 01:02:08 MST
2 April 2003 JOHN WHITFIELD
terms.
© alamy.com
Belgian biologist has discovered. The Superformula, as its creator Johan
Gielis has christened it, produces everything from simple triangles and
pentagons, to stars, spirals and petals.
computer," says Gielis, at University of Nijmegen, Holland. "It seemed too
good to be true - I spent two years thinking 'What did I do wrong?' and 'How
come no one else has discovered it?'" Having spoken to mathematicians, he
reckons that he's found something new.
Changing one term in the formula varies the proportions of the shape - moving
from a round circle to a long and skinny ellipse. Changing another varies the
axes of symmetry - shifting from a circle to triangle, square, pentagon and
so on.
of sides, regular and irregular. It can also produce three-dimensional
structures, and non-biological shapes such as snowflakes and crystals. "It's
a new way of describing nature," says Gielis.
spiral of a sheep's horn, the branching of a tree, or a bee's honeycomb - in
mathematical terms.
botanist Karl Niklas of Cornell University in Ithaca, New York. Researchers
have come up with many ways to describe leaves and shells, for example, but
there is little unity: "Things have become cumbersome and idiosyncratic," he
says.
comparing the shapes of life, believes Niklas. "This is an exciting
development."
sides.
© J. Gielis
Gielis has patented his discovery, and is developing computer software based
on it. Using one formula to produce shapes will make graphics programs much
more efficient, he says. It might also be useful in pattern recognition.
shapes. "I'm not convinced this is significant, but it might turn out to be
profound if it could be related to how things grow," says mathematician Ian
Stewart of the University of Warwick, UK.
shapes, says Stewart. He believes that the Superformula is more likely to
provide a useful tool than an insight into how life actually works.
it got there, but he hopes that time might prove the Superformula's
profundity. "Description always precedes ideas about the real connection
between maths and nature," he says.
References
natural and abstract shapes. American Journal of Botany, 90, 333 - 338,
(2003). |Article|