Patterns with regular shapes turn up all over the place. You can see them as epidermal ridges on the tips of your fingers, as zebra stripes or as the beautiful architecture of the seeds at the center of a sunflower.

Some folk give teleological arguments for their presence: The ridges on your fingertips give you better feel; the stripes on animals provide camouflage; the seeds on the sunflower head are positioned so that each has the most space possible and therefore best access to nutrients and light.

Now it may very well be that such patterns provide evolutionary advantage so that in the long run, striped zebras are more likely to survive than zebras without markings.

But that is not how the patterns were made.

To understand the hows, we must understand the physical and mechanical processes that lead to pattern formation. As they shrink, the volar pads on what will become fingertips contract and wrinkle, creating fingerprint patterns. Interactions between two different chemical substances can lead to the domination of one over the other in neighboring stripes. In plants, the biochemistry leads to a nonuniform distribution of a growth-promoting hormone, auxin. The seeds are initiated at the locations where the auxin concentration is largest.

Along with many other interests in ocean waves and in optics, I have long been interested in how patterns form and how best to describe them. In the last decade, my investigations with colleagues Patrick Shipman, Zhying Sun and Matt Pennybacker have centered on phyllotaxis: the configurations of seeds on a sunflower head, of spines on the saguaro cactus, of bracts on pinecones. What is truly astonishing is that although many of the properties of plant patterns have been known for more than four centuries, it is only in recent years that widely accepted explanations have begun to emerge.

One of the magic properties of plant patterns is that these numbers belong to a very special set called Fibonacci numbers. Fibonacci sequences are generated by starting with any two numbers, say 1 and 2, and computing each successive member of the sequence by adding the last two. On the sunflower shown, you can count 34 and 55 clockwise and anticlockwise spirals respectively at the outer edge, numbers which belong to the most common Fibonacci sequence 1,2,3,5,8,13,21,34,55,89... .

We have used our experimentally informed mathematical model to reproduce the configuration of auxin maxima within a sunflower and, hence, the likely sites for seed initiation.

The wonderful surprise is this: The places where our model says the seeds should be are the very same as those positions which an algorithm based on the teleological model would predict. The patterns that nature creates using plain old physics and chemistry are the means by which organisms can pursue optimal strategies. How great is that!

Look around you and marvel at the patterns of life’s architectures on fingertips, sunflowers, sand-ripples and seashells. Wonder how they were made and what advantages they provide. Embrace and revel in their beauty.