EPOW - Ecology Picture of the Week

Each week a different image of our fascinating environment is featured, along with a brief explanation written by a professional ecologist.

17-23 November 2003

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Fibonacci Spirals Are Everywhere


Fibonacci or Logarithmic Spiral in Cone Shell

Credit & Copyright: Dr. Bruce G. Marcot
Explanation:  It seems to be everywhere in nature!  It's the Fibonacci spiral, a pattern that follows the Fibonacci sequence of numbers:  0,1,1,2,3,5,8,13... where the next number is simply the sum of the previous two numbers.

Also called the Bernoulli spiral, logarithmic spiral, equiangular spiral, and other names, it forms on shells, flowers and seed heads, pine cones, ears, pineapples, and many other formations.  

This sequence may account for the apparent "self-similarity" of patterns found in many phenomena in nature -- like the logarithmic spiral of land snails (such as shown in the zoom animation at right shown at 10x, 60x, and 200x), the spiral of ancient nautilus shells, the patterns of reproduction of rabbits, and even patterns of hurricanes and galaxies

"Self-similarity" refers to how many patterns in nature seem the same whether  zoomed in or out, and was a major revelation when Mandelbrot's "fractal geometry of nature" was first applied to describing natural phenomena. In fact, it has been discovered that fractals hide Fibonocci numbers!

The simplest form of self-similarity in nature seems to be from the Fibonacci spiral, which occurs as an organism grows such that its  proportions remain constant.  

It is a simple recurrence of pattern and ratios that create beautiful forms.  With Fibonacci spirals you can ponder the meaning of life, explain patterns in nature, or just have fun

AddendumAre Fibonacci spirals really everywhere?  I appreciate some rather pointed emails from Donald Simanek challenging this idea.  He has posted an interesting essay suggesting that many (or most) instances of Fibonacci spirals are specious interpretations of other patterns.  
     He agreed with me that such spirals arise (and are generally isomorphic) when growth is constrained by shape so that proportions are maintained as growth proceeds.  This may be the cause of apparent, and often superficial, underlying similarity among different entities ostensibly exhibiting the general Fionacci "rule."  Check out his essay (linked above) for further critique of the idea.


Next week's picture:  Life on the Ice

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