Perhaps nature simply had no choice: the shape is decided by the dictates of physical forces

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Perhaps the most curious thing about natural patterns is that they come from a relatively limited palette, recurring at very different size scales and in systems that might seem to have nothing at all in common with one another.


The world is a confusing and turbulent place, but we make sense of it by finding order. We notice the regular cycles of day and night, the waxing and waning of the moon and tides, and the recurrence of the seasons. We look for similarity, predictability, regularity: those have always been the guiding principles behind the emergence of science. We try to break down the complex profusion of nature into simple rules, to find order among what might at first look like chaos. This makes us all pattern seekers.

It’s a habit hardwired into our brains. From a baby’s first inklings of repeated sounds and experiences, recognizing pattern and regularity helps us to survive and make our way in the world. Patterns are the daily bread of scientists, but anyone can appreciate them, and respond to them with delight and wonder as well as with aesthetic and intellectual satisfaction. Just about every culture on earth, from the ancient Egyptians to Native Americans and Australian Aborigines, has decorated its artifacts with regular patterns. It seems that we find these structures not only pleasing but also reassuring, as if they help us believe that, no matter what fate brings, there is a logic and order behind it all.

But when we make our own patterns, it is through careful planning and construction, with each individual element cut to shape and laid in place, or woven one at a time into the fabric. The message seems to be that making a pattern requires a patterner. That’s why, when people in former times recognized patterns in nature—the bee’s honeycomb, animal markings, the spiraling of seeds in a sunflower head, the six-pointed star of a snowflake—they imagined it to be the fingerprint of intelligent design, a sign left by some omnipotent creator in his handiwork.

Background created by fractal geometry.

Today, we don’t need that hypothesis. It’s clear that pattern, regularity, and form can arise from the basic forces and principles of physics and chemistry, perhaps selected and refined by the exigencies of biological evolution. But that only deepens the mystery. How does the intricate tapestry of nature contrive to organize itself, producing a pattern without any blueprint or foresight? How do these patterns form spontaneously?

There are clues in how they look. Perhaps the most curious thing about natural patterns is that they come from a relatively limited palette, recurring at very different size scales and in systems that might seem to have nothing at all in common with one another. We see spirals, say, and hexagons, intricate branching forms of cracks and lightning, spots and stripes. It seems that there are types of pattern-forming process that don’t depend on the detailed specifics of a system but can crop up across the board, even bridging effortlessly the living and the non-living worlds. In this sense, pattern formation is universal: it doesn’t respect any of the normal boundaries that we tend to draw between different sciences or different types of phenomena. (Pg.11)

Growth and form?

Do these patterns have anything in common, or is the similarity in their appearance just coincidence?

The first person to truly grapple with that question was the Scottish zoologist D’Arcy Wentworth Thompson. In 1917 Thompson published his masterpiece, On Growth and Form, which collected together all that was then known about pattern and form in nature in a stunning synthesis of biology, natural history, mathematics, physics, and engineering. As the title indicates, Thompson pointed out that, in biology at least, and often in the non-living world, pattern formation is not a static thing but arises from growth. “Everything is what it is,” he said, “because it got that way.” The answer to the riddle of pattern lies in how it got to be that way—how the pattern grew. That’s less obvious than it sounds: a bridge or a paddy field or a microchip is “explained” by how it looks, not by how it was made.

Part of Thompson’s agenda was to put a brake on the runaway enthusiasm that had developed at that time for explaining all form and order in the living world by invoking Charles Darwin’s theory of natural selection—to say that the pattern was there because it served some adaptive purpose in helping the organism to survive. Not necessarily, Thompson cautioned. Perhaps nature simply had no choice: the shape is decided by the dictates of physical forces, not by the convenience for biology. Even living creatures have to be soundly engineered to withstand the whims of fate. It was a timely reminder of the constraints on Darwin’s theory, but it doesn’t actually conflict with it. In the living world, pattern formation seems both to restrict the options for adaptive change and to offer new adaptive opportunities—to operate, in other words, in parallel and sometimes in sympathy with Darwinian evolution. It supplies, for example, the color markings that animals put to striking use for camouflage, or as warning signs to predators, or so that members of a species can recognize each other. These patterns might not be arbitrary, but they can be useful. (Pg.13)

These patterns affirm, too, what the American physicist Richard Feynman said about the workings of the universe: “Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.” The principles that operate in the world are general ones, and you can sometimes read them as clearly in a small corner as in a big vista: in a saucepan on the stove, you might see an intimation of the convection patterns that arrange the clouds across the sky, for example, while the network of veins in your body echoes (for good reason) the great river networks that cross continents and shape mountain ranges. This doesn’t mean to say that one grand theory explains all these things, although some scientists have dreamed, and still dream, of such a thing. But it does make many patterns variations on a theme, and reflects the fact that they often arise from broadly similar processes—ones in which some driving force, be it gravity or heat or evolution, prevents the system from ever settling into a steady, unchanging state; in which various influences interact with each other, sometimes reinforcing and sometimes competing; in which patterns and forms might switch abruptly to a new shape and appearance when the driving force exceeds some threshold value; in which small events can have big consequences and what goes on here can influence what transpires at a distant point there; and in which accidents may get frozen into place and determine what unfolds thereafter. There is no Law of Pattern Formation, but there is perhaps a recipe book. (Pg15)

— Patterns in Nature: Why the Natural World Looks the Way It Does by Philip Ball

WE&P by: EZorrilla


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