Spiral Distribution of Seeds on a Flower

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 Created by webMathematica , you get the same result as you would with the fractional part of the number. Therefore, Created by webMathematica (Pi in Mathematica) is the same as Created by webMathematica

  • Incremental angle for successive seeds:
  • Number of seeds
    • 100 seeds
    • 500 seeds
    • 1000 seeds
    • 4000 seeds
  • Color

Ken Levasseur
Mathematical Sciences
UMass Lowell
UML WebMathematica Scripts Notes on Mathematica