Numerical Flowers

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This generalizes how seeds are distributed on plants such as sunflowers. Starting from the center, each successive seed is a fixed distance from the previous seed and is rotated from the line connecting the previous two seeds by a constant angle. Using the controls, you can explore how different angles, , produce varying patterns with seeds.

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The angle is represented as a percentage of a full rotation, so 45 degrees would be 1/8. If you enter a number greater than one, you get the same result as you would with the fractional part of the number. Therefore, is the same as .

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Contributed by: Ken Levasseur (UMass Lowell) (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

M. Naylor, "Golden, , and Flowers: A Spiral Story," Mathematics Magazine, 75(June), 2002 pp. 163-172.



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