Mathematical Budding Model Revealed in a Lily

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"Earth laughs in flowers," Ralph Waldo Emerson said, but flowers laugh in numbers, according to two Harvard mathematicians who have modeled the blossom song of the Asiatic lily.

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The new model for flower blooming overturns previous ideas of how the delicate structures unfold themselves.

Earlier models had explained blooming through different growth rates between the inner and outer layers of petals or motion in the midrib.

This new research shows that, as William Carlos Williams said, "It is at the edge of a petal that love waits."

The flower petals burst forth from their buds by elongating their edges more than their middles, the mathematicians found. The outside edges grow up to 40 percent more than the interior midrib, which causes the petals to wrinkle.

The wrinkling creates stresses in the bud until there comes a time when, as Anais Nin said, "the risk to remain tight in the bud was more painful than the risk it took to blossom."

The stresses force the bud to open, and the petals then curve and curl into the shapes that humans find so beautiful.

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The new wrinkly-edge model not only helps scientists understand how flowers open but could lead to advances in bio-mimicry, or the engineering of devices based on models from nature, such as thin-film motors and actuators.

To understand how flowering happens, Haiyi Liang and L. Mahadevan, the Harvard researchers who conducted the study, marked lily buds with a series of dots, then watched as they opened in a time-lapse video.

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The scientists then developed a mathematical model to explain what they had observed.

IMAGE 1: The Asiatic Lily (Lilium casablanca) (WIKIMEDIA COMMONS).

IMAGE 2-4: The Asiatic Lily blooming (PNAS).

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