Sunflowers show complex Fibonacci sequences

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Sunflowers show complex Fibonacci sequences

Mathematical biologists love sunflowers. The giant flowers are one of the most obvious—as well as the prettiest—demonstrations of a hidden mathematical rule shaping the patterns of life: the Fibonacci sequence, a set in which each number is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, ...), found in everything from pineapples to pine cones. In this case, the telltale sign is the number of different seed spirals on the sunflower's face. Count the clockwise and counterclockwise spirals that reach the outer edge, and you'll usually find a pair of numbers from the sequence: 34 and 55, or 55 and 89, or—with very large sunflowers—89 and 144. Although the math may be beautiful, plant biologists have not worked out a mechanistic model that fully explains how the sunflower seed patterns arise. The problem is that plants don't always show perfect Fibonacci numbers—real life is messy—and data on real sunflower diversity is scarce. So the Museum of Science and Industry in Manchester, U.K., crowdsourced the problem. Over the past 4 years, members of the public have been growing their own sunflowers and submitting photographs and counts of the spiral patterns. After verifying the counts from 657 flowers, a more realistic picture of sunflowers is emerging. A study published today in Royal Society Open Science reports that nearly one in five of the flowers had either non-Fibonacci spiraling patterns or patterns more complicated than has ever been reported, including near-Fibonacci sequences and other mathematical patterns that compete and clash across the flower's face. The possibility of capturing sunflower development with math just got more realistic—and more complicated.