Sunflower Seed-head, Real and Simulated

October 15, 2011


Photographer: Greg Parker
Summary Author: Greg Parker

Recent gales brought down some of the biggest sunflowers in my garden, so I took the opportunity of this sad event to take a few macroscopic photos of the sunflower seed-heads. My research into photonic devices led me to discover that the sunflower seed-head pattern has infinite rotational symmetry. Clearly, part of the research needed me to be able to simulate the sunflower seed-pattern, which you can see at right.  This is a plot produced using Mathcad 2000 software -- the X-Y coordinates of each point are directly related to the Golden Ratio phi. The ratio is 1.6180339887499... and is represented by the Greek letter phi. This proportional value exists in seashells, like the nautilus, and in many flowering plants, like pineapples and pine cones. The Golden Ratio is a truly remarkable number, not only is it an irrational number, it's the most irrational, irrational number as well!  There's a great deal of mathematics to be discovered in a sunflower seed-head. Photo taken in early September 2011 in Southampton, England.