Your Backyard Contains a Kaleidoscope, If You Know Where to Look Demystifying Nature's Kaleidoscope

Surface tension is one of nature’s form-creating agents. Here it pulls water droplets into almost spherical beads as they sit on the waxy, water-repellent surface of a leaf.

(Olgysha, Shutterstock.com)

Philip Ball, who has written about everything from music to molecules, normally doesn’t care to revisit his subjects. But he’s come back to the natural world’s visual repetitions over the past 15 years, most recently with Patterns in Nature, which Publisher’s Weekly calls the “most beautiful book of 2016.” (So far, at least.)

His photo-rich book will likely change how you look at a snail’s shell, a leaf with dew drops on it, or really anything else that nature places in your sightline, including your own fingertips. Here, Ball shares what he’s observed in more than 15 years of examining the science behind nature’s beauty.—Christina Nunez

Finding pure mathematics in a sunflower

There’s an awful lot of interesting math in [nature’s patterns]—for example, in the so-called Fibonacci patterns that you see on the heads of sunflowers. This has fascinated mathematicians for a long time, just as it’s fascinated botanists for a long time. What on earth is this pure math doing in nature? That’s one of the reasons that mathematicians are drawn to this.

You also find literally the same math describing very different systems. You can describe the formation of patterns on animal skins in terms of mathematical equations. You can also use those equations to understand dynamics of populations of predators and their prey, how the size of the different populations goes up and down, and how that depends on the populations are spread through a territory. [It’s] basically a math about how things reproduce and how things spread out, those are the key processes that are going on in both of those cases. (Launch the full gallery of photos from the book.)

12 Wondrous Photos of Patterns in Nature
See examples of nature's creativity with 12 photos from Philip Ball's book and read more from an author interview here.
Snail shell
The logarithmic spiral, which gets ever tighter towards its center, is found throughout nature, from snail shells to tropical cyclones to spiral galaxies. It is a self-similar shape: as you zoom in towards the center, the spiral always looks the same. (Captions by Philip Ball, photos courtesy University of Chicago Press)
Wasp on a nest
Some wasps build nests out of chewed-up wood fibers in which the cells have perfectly hexagonal cross-sections. They have inherited instincts for making this geometrical pattern, which packs the cells together with the minimum of wall area.
Sand dune
Sand dunes take many forms, but all arise from the spontaneous self-organization of wind-blown sand. These undulating forms are called seif dunes.
Molten cracks
Cracks in a molten material appear as the top layer cools, solidifies and contracts, creating stresses in the hard layer. As the cracks relieve stress, they join up into a network that, while not perfectly orderly, obeys certain geometric rules about how cracks intersect.
Mollusk shell
The spiral shells of mollusks are really just a way of growing an ever larger chamber at the shell mouth for the soft organism to live in, without having to change the chamber’s basic shape.
Butterfly wing
The colored markings on butterfly wings are made up of thousands of individual scales with distinct colors. Common pattern elements, like stripes and eyespots, are reshuffled in different species with seemingly endless variety and invention.
Millipede
The logarithmic spiral can also be considered to be a kind of rolled-up cone, like the gently tapering body towards the tail end of a millipede.
Bubbles
In a normal foam, not all bubbles have the same size and shape, nor do they all have the same number of polygonal sides. But there are geometrical rules that govern bubble intersections: in particular, three bubble walls meet at angles of about 120 degrees, like the Mercedes sign.
Dewy leaf
Surface tension is one of nature’s form-creating agents. Here it pulls water droplets into almost spherical beads as they sit on the waxy, water-repellent surface of a leaf.
Compound eye
The compound eyes of flies look like a raft of bubbles floating on the water surface: both are arrays of tightly packed hexagons.
Butterfly wing: microscopic view
Seen close up, the scales of butterfly wings are themselves delicately patterned with microscopic grooves and channels. Light reflected from these tiny structures undergoes wave interference, which picks out some colors at the expense of others and gives the wings an iridescent hue.
Mineral dendrites
So-called mineral dendrites—dark branching patterns in rocks—look like fossil plants, and have sometimes been mistaken for them. But they are non-living crystals that have grown into this shape through a delicate balance of spreading and precipitation of the chemical ingredients.

How scientists began to crack the code

From the 1970s to the 1990s, you could argue that this field was cracked [open]. It was really only then that we had the conceptual tools, a lot of which came out of physics, but also the computational tools. You could start modeling these things on computers in very detailed ways. We only then had the tools to really understand questions that scientists of all description had been grappling with for hundreds of years, if not thousands of years—the Greeks were fascinated by them.

Nature just throws out all these beautiful variations on a theme. There’s something astonishing in that.

Alan Turing saw it early on

We’re now understanding that the mechanisms [for patterns] seem to operate in biochemical systems. Ultimately the rules have to be genetically encoded. You see them in the wrinkles on your fingertips, you see them probably in the pattern of hair follicles on the back of your hand. They’re fairly evenly spaced apart, even though they’re not perfectly regular. You see them in the grooves on the upper part of a dog’s palate. All of these systems are ones that biologists over the past 10 years or so have got to grips with.

These are called reaction diffusion systems, and the way that they can form patterns was first really explored by the mathematician Alan Turing in the 1950s. He wrote a seminal paper on this subject that was way before its time. It wasn’t really until the 1970s, and particularly the 1980s and ‘90s, that people started to understand the basis of what Turing at laid out and define systems where it really did seem to apply.

What we have in common with ice

Living systems are highly patterned. That’s how you get from a single, pretty much spherically symmetrical cell to this complex organism that’s us, or that’s a fly or that’s a flower. That is a patterning process. So it’s literally true that the formation of these patterns has complete relevance to how life sustains itself—and quite probably to how life appeared in the first place.

The fact that those same mechanisms are working in non-living systems, there is something poetic and beautiful in that. It’s a kind of unifying principle. You can intuit that most clearly with snowflakes: They have this incredible intricacy far beyond what seems reasonable for a bit of ice forming in air to acquire. We understand now how that process works, but I think all the same it’s proper for us to continue to see that with some wonder.

Nature’s inherent creativity

I’d argue that there’s a real sense in which we can see nature as being creative there. That it has a patterning mechanism but it produces these endless variations without any effort it seems on nature’s part, just throws out all these beautiful variations on this theme. There’s something astonishing in that.

Comments have been edited for length and clarity.