Spirals in Nature

And in the Parthenon, perhaps

Trace the bracts of a pinecone, the arrangement of seeds in a sunflower, the patterns of galaxies in the sky, the turn of a snail shell, or your inner ear cochlea – and you will find spirals. In fact, once you start becoming aware of spirals in nature, you are likely to see them everywhere.

Is this a pattern? Or just coincidence?

Spirals can be described mathematically by the Fibonacci sequence, a sequence in which each number is the sum of the two that came before it. The sequence goes like this: 0,1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… and so on. The graphic below shows a tiling made up of squares whose side lengths are successive Fibonacci numbers. When you draw circular arcs through the corners of those squares, you get the Fibonacci spiral that is observed so often in nature:

an illustration of a spiral based on the Fibonacci sequence — Graphic by Romain (Own work, CC BY-SA 4.0)

But can plants count? Do they deliberately lay their leaves along a stem to follow this mathematical progression? No one really knows, but some speculate that it is nature’s way of allowing as much light as possible to reach each leaf. In fact, it would be surprising if plants did not maximize the potential for their leaves to access sunlight through the use of the Fibonacci sequence.

Wabanaki art often features spirals through the “recurve” motif that can be found in birch bark etchings and other traditional work. It was explained to me that this is because of the importance of spirals in nature – the fern frond, the pattern of scent a deer lays before bedding down, in order to be able to detect a predator regardless of wind direction – and the power of this pattern.

Wabanaki recurve design on the side of a birch bark canoe — A traditional Wabanaki recurve design etched onto the sides of a birch bark canoe

The Fibonacci sequence is very closely related to the golden number (1.61803399), otherwise known as the golden ratio. When dividing a number in the Fibonacci sequence by the one that comes before it, the result will become closer and closer to 1.618. While sometimes a point of contention among mathematicians, many believe that the Parthenon, the Egyptian pyramids, the Taj Mahal, and many other great architectural works reflect this golden ratio, which creates proportions that are balanced and pleasing to the eye.

If you want to see some short, fun videos that describe the Fibonacci sequence and its occurrence in plants, I recommend a set of videos by “Vihart” called “Doodling in Math: Spirals, Fibonacci, and Being a Plant.”

And from now on, as you encounter spirals in nature, you might reflect on the power in that shape – and wonder if perhaps it could not be any other way.