Endless Variations on a Theme

As my perceptions become more acute on this journey into nature, I am more and more in awe of the endless variety of plant shapes and patterns of growth and how/why they evolved. For example, I attempted to "key" out a huge white flowering "weed" found near the C&O Canal towpath near Harper's Ferry, WV this spring. Using the Newcomb's Guide to Wildflowers, I wasn't having much luck, until I realized the plant's resemblance to Queen Anne's Lace (an alien import). I broke off a leaf, crumbled it, sniffed it, even tasted it! Yep, that carroty scent. (Queen Anne's Lace is known as a wild carrot.) This led me to the right page in the book.

The plant was in the parsley family-a common species known as Cow Parsley (Anthriscus sylvestris) a native to Europe, Africa and Asia, that often grows to over six feet. Since Newcomb's Guide uses a keying method that is based on numbers of petals and leaves and their arrangement, I decided to count the stems in the umbel, and came up with 29. That seemed wierd, so I counted again. And again. Still 29. That brought up the question: what is the "math" behind nature's botanical design?

I had heard about Fibonacci numbers but had never studied them. Fibonacci was a mathematician in the Middle Ages. The numbers emerged as he studied the reproduction patterns of rabbits! The numbers are an infinite series, beginning with the numeral 1, where each successive number is the sum of the two numbers that appear directly before it. Design based on these proportions approximates the "golden ratio," also known as the golden mean, golden number or divine ratio. Expressed as a decimal, the golden ratio is approximately 1.6 , referred to as Phi.

Growth patterns that follow the golden ratio are rampant in nature. Two examples often cited are the spirals of a nautilus shell and seed head of a sunflower. The golden ratio is seen as well in the proportions of the human body--even the structure of DNA is a demonstration of the golden ratio. Not surprising that in classic art and architecture, the golden ratio was considered to be the foundation of beauty.

But back to Cow Parsley. The number 29 was not listed in the Fibonacci series of numbers. But there is another series that models the golden ratio, developed by Lucas, the mathematician who "discovered" Fibonacci's work. This series of numbers is also very prevalent in the growth patterns of plants. The Lucas series replicates the "sum of the previous two numbers" feature, but starts with 2 followed by 1. And there it was, my Cow Parsley's "29." Amazing what trying to identify a weed can lead to....! Now I see the golden ratio everywhere, as in the thistle bud at top.