Spiral Distribution of Seeds on a Flower
Spiral Distribution of Seeds on a Flower |
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In the June 2002 issue of the Mathematics Magazine, Michael Naylor has an excellent article titled "Golden, Sqrt[2], and Pi Flowers: A Spiral Story." In it, he discusses how seeds are distributed in a spiral pattern on plants like a 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. In this script, you can explore how different angles produce varying patterns. See Prof. Naylor's paper to see what the "best" angle - the one Mother Nature appears to use.
The angle is entered below as a percentage of a full rotation, so 45 degrees would be 1/8. If you enter a number greater than one, such as the default value of , you get the same result as you would with the fractional part of the number. Therefore,
(Pi in Mathematica) is the same as