Strawberries
Strawberries
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Rows of seeds in strawberries are tricky to count, even when looking at the fruit from below or unrolling it digitally.
Smith students, using methods developed in the Plant Math Lab, analyzed a sample of some 40 wild strawberries found on campus. The number of spirals concentrated around (19, 19), with many being (18, 19), (19, 18), (19, 20) or (20, 19). This fits a pattern the book's co-authors call "quasi-symmetric."
(Photos by Stéphane Douady)
Spiral numbers in wild strawberries: quasi-symmetry
Spiral numbers in wild strawberries: quasi-symmetry
Smith students Bella Bandura, Cecilia Friedman, Raenen Traver-Fallick, and Hualong Xu "unrolled" 40 wild strawberries. Using programs that detect zigzag fronts, they counted spirals at different levels of each strawberry.
The x-axis shows the number of counter-clockwise spirals, while the y-axis counts the clockwise spirals. Note the concentration near the diagonal, where these numbers are the same. This is a clear sign of quasi-symmetry.
Spiral numbers in magnolias: Fibonacci
Spiral numbers in magnolias: Fibonacci
The same students, plus Amelia Tarno, analyzed more than a hundred flower buds from several different Magnolia trees.
Here the spiral numbers are concentrated at (3, 5), (5, 3), (5, 8) and (8, 5), located near the lines whose slope is the golden ratio or its inverse. This is a solid example of Fibonacci pattern.
One tree also showed (4, 6) and (6, 4) patterns, called bijugate because it displays Fibonacci pairs—here (2, 3) and (3, 2)—times 2 .
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