Works in Progress - Winter 2013

Leaf It to a Physicist

By Sam Kean | March 14, 2013
Jon Sullivan
Jon Sullivan


Your mental image of an oak leaf may differ considerably—and accurately—from that of someone who grew up in another part of the country. Some leaves are roughly circular. Others have rounded lobes, and still others are saw-toothed. Such diversity has puzzled biologists because all oaks are closely related. But new research suggests that a single mathematical formula can explain most leaf variety, in oaks and other trees.

David Young of the Lawrence Livermore National Laboratory in California devised the formula. He is a physicist who, he says, has dabbled in biology for decades. First Young selected an equation that, when graphed, could produce the outline of a basic leaf shape—a broad oval, pointed at the tip. Next he explored how internal structures, especially leaf veins, affect that outline. Veins control and guide most leaf growth, and fiddling with variables for the number, position, and direction of the veins allowed him to produce more complicated shapes, like serrations.

Young entered his equation into a computer and ran simulations in which he held some variables constant and altered others. Each simulation took just a second, but he found that his equation could indeed reproduce the range of leaf shapes in many species, including poplars, willows, birches, magnolias, ginkgos, elms, and oaks. It also worked for herbaceous plants such as cockleburs and morning glories.

As a next step, Young says he might delve into the genetics and evolution of leaf growth. Or he might investigate maples, whose 130 species show incredible leaf variety, or begonias, whose leaves curl exotically. Regardless, his foray into leaf shape has given him a deeper appreciation of the simplicity behind nature’s complexity. Nowadays, he says, “I am looking at and enjoying leaves more.”

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