New ways of looking at the world help explain the development of complex and beautiful patterns in nature

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. But 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 the patterns in the world around us?

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 honey bee's remarkable architectural abilities.

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