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Designed by Nature
| Article
# : |
10830 |
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Section : |
NATURAL SCIENCE
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| Issue
Date : |
3 / 1993 |
1,757 Words |
| Author
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Scott Camazine
Scott Camazine is a biologist, physician, and photographer.
He studies self-organization and pattern formation in honeybee
colonies at Cornell University. He has written two books
about nature: The Naturalist's Year and Velvet Mites and
Silken Webs (John Wiley & Sons). |
A hike in the woods or a walk along the beach reveal an endless variety of forms. Nature abounds in spectral colors and intricate shapes: the rainbow mosaic of a butterfly's wing, the delicate curlicue of a grape tendril, the undulating ripples of a desert dune. These miraculous creations not only delight the imagination, they also challenge our understanding. How do these patterns develop? What sorts of rules and guidelines shape them?
Some patterns are molded with a strict regularity. At least superficially, the origin of regular patterns often seems easy to explain. Thousands of times over, the cells of a honeycomb repeat their hexagonal symmetry. The honeybee is a skilled and tireless artisan with an innate ability to measure the width and to gauge the thickness of the honeycomb it builds. Although the workings of an insect's mind may baffle biologists, the regularity of the honeycomb attests to the honeybee's remarkable architectural abilities.
The nautilus is another meticulous craftsman, who designs its shell as a logarithmic or equiangular spiral. This precise curve develops naturally as the shell increases in size but does not change its shape, ever growing but never changing its proportions. The process of self-similar growth yields a logarithmic spiral. We find the same spiral in the horns of mountain sheep and in the path traced by a moth drawn toward a light. For the mathematically inclined, such a curve can be succinctly described by the formula r = c raised to the power of theta, where r is the radius of the curve, c is a constant, and theta is the angle through which the curve has revolved.
Crystals are likewise constructed with mathematical regularity. A chemist could readily explain how positively and negatively charged sodium and chloride ions arrange themselves neatly in a crystal lattice, resulting in salt crystals with a perfect cubic structure. And water molecules, high in the clouds with temperatures below freezing, neatly coalesce to form crystalline snowflakes in the form of six-sided stars or hexagonal needles.
Although some of nature's artistry is no longer a mystery, other patterns are more subtle and perplexing. They may possess mathematical regularity, but that does not help explain how they form. Consider the Fibonacci sequence, named after the medieval Italian mathematician Leonardo Fibonacci. Begin with 0 and 1. To obtain each succeeding number in the series, simply take the sum of the previous two numbers. The result is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89… and so on.
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