Golden Spirals

April 19, 2013

Golden_Spiral

Photographer: Greg Parker
Summary Author: Greg Parker

April 2013 Viewer's Choice In an earlier Earth Science Picture of the Day we showed how a sunflower seed head followed a Fibonacci pattern in the distribution of its seeds within the seed head. Here we show how another geometric form related to the Fibonacci series, the logarithmic spiral, also makes an appearance in Nature. The polar equation for the logarithmic spiral is:

r = a e^ϴ

Where r is the distance from the origin; ϴ (theta) is the angle made with the x-axis; a is an arbitrary constant.

The MathCad program was used to generate logarithmic plots (in cyan) which are placed next to the appropriate natural object. At center is shown a Nautilus shell (present day) and on either side of it are the two halves of an ammonite (extinct) that’s been sawn through to show the inner structure. Ammonites were marine, invertebrate animals that lived around 100 million years ago; whereas the modern Nautilus is a marine mollusk of the cephalopod family Nautilidae. The Golden Spiral has thus been a useful growth template for Nature over millions of years. Note that it can also be seen at a much larger scale in the structure of some spiral galaxies.