Sunflowers Do the Math
The spiraling shapes in cauliflower, artichoke, and sunflower florets (above) share a remarkable feature: The numbers of clockwise and counterclockwise spirals are consecutive Fibonacci numbers—the sequence 1, 1, 2, 3, 5, 8, and so on, so that each number is the sum of the last two. What’s more, those spirals pack florets as tight as can be, maximizing their ability to gather sunlight for the plant. But how do plants like sunflowers create such perfect floret arrangements, and what does it have to do with Fibonacci numbers? A plant hormone called auxin, which spurs the growth of leaves, flowers, and other plant organs, is the key: Florets grow where auxin flows. Using a mathematical model that describes how auxin and certain proteins interact to transport each other around inside plants, researchers could predict where the hormone would accumulate. Simulations of that model reproduced patterns exactly matching real “Fibonacci spirals” in sunflowers, the team reports this month in Physical Review Letters. Based on their results, the researchers suggest that such patterns might be more universal in nature than previously thought, so keep an eye out: Fibonacci numbers might be spiraling in every direction.
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An Illustration of Vogel’s model for the pattern of florets in the head of a sunflower.
