 The florets of romanesco follow the Fibonacci spiral
Image credit: M. King

The Fibonacci spiral, or Golden spiral, comes directly from the Fibonacci sequence, a pattern of numbers popularized (but not discovered (1)) by Italian mathematician, Leonardo Fibonacci. The Fibonacci sequence is a series of numbers whereby any number in the series (besides 0 and 1, the first two numbers in the sequence) is the sum of the previous two numbers (2).

The spiral design is drawn as an arc connecting opposite corners of squares with lengths that correspond to each consecutive Fibonacci number (3).

Ever since I was a kid, I was enthralled with the Fibonacci sequence. I wasn’t interested in any of the “mystical powers” that the sequence purportedly has (at least in popular culture.) Rather, I always just saw it simply as “something cool” like Sum of Some. In fact, I was so interested in it, in fact, that I did write programming code (in Ruby) that finds the nth Fibonacci number.

Despite my allergy to the notion that the Fibonacci sequence knows all, explains all, is all, I do find it pretty cool that it does show up in nature from time to time. The purpose of this essay is simply to celebrate its appearance in nature. Below are a few plants (and one animal, a mollusk) that illustrate the Fibonacci sequence. This is not an exhaustive list. The Fibonacci sequence can be found in the arrangement of leaves on the stalk of a sunflower (and other plants), the parentage of honeybees, chamomile, pineapples, the curling of ferns, artichokes, the curves of waves, etc (4) The arrangement of seed scales on a pine cone
Image credit: Daniel Oines The cross section of a nautilus shell
Image credit: Jitze Couperus The Fibonacci sequence can be found in the arrangement of coneflower seeds.
Image credit: Patrick Standish The arrangement of seeds on a sunflower
Image credit: Robert Benner

References:

1. “Toward a Global Science”, Indiana University Press, Goonatilake, Susantha
2. “Fibonacci Numbers and the Golden Section”, University of Surrey, Knott, Ron
3. “The Fibonacci Sequence, Spirals and the Golden Mean”, Temple University, Reich, Dan
4. “Fibonacci Statistics in Conifers”, Fibonacci Quarterly, Brousseau, A