Philip Ball's Patterns in Nature is a jaw-dropping exploration of why the world looks the way it does, with 250 color photographs of the most dramatic examples of the “sheer splendor” of physical patterns in the natural world. Ball picks out some of the highlights.

I’m the kind of writer who likes to move on. Once I’ve covered a topic, I have no strong desire to return to it in subsequent books. Yet with Patterns in Nature I have revisited the subject of natural pattern formation for the third time.

It began in 1999 with The Self-Made Tapestry, in which I explained the science of how pattern and regular form arise spontaneously in nature, through no foresight or design. Years later I found myself repeatedly asked how to get hold of a copy of the now out-of-print volume, so I suggested to Oxford University Press that we publish a revised edition. That bloomed into a 2009 trilogy, much of which was entirely new: Nature’s Patterns: Shapes, Flow, Branches.

And yet… The topic is inherently visual, concerned as it is with the sheer splendor of nature’s artistry, from snowflakes to sand dunes to rivers and galaxies. But I was frustrated that my earlier efforts, while delving into the scientific issues in some depth, never secured the resources to do justice to the imagery. This is a science that, heedless of traditional boundaries between physics, chemistry, biology and geology, must be seen to be appreciated. We have probably already sensed the deep pattern of a tree’s branches, of a mackerel sky laced with clouds, of the organized whirlpools in turbulent water. Just by looking carefully at these things, we are halfway to an answer.

I am thrilled at last to be able to show here the true riches of nature’s creativity. It is not mere mysticism to perceive profound unity in the repetition of themes that these images display. Richard Feynman, a scientist not given to flights of fancy, expressed it perfectly: “Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry.”

Waves of pigmentation. As mollusk shells grow, pigmented material is sometimes laid down along the rim. If there are periodic bursts of pigmented and unpigmented growth, the result is banding perpendicular to the axis of the conical shell. If pigmentation happens at fixed spots around the rim, the result is stripes parallel to this axis. And if the pigmentation occurs as waves that progress steadily around the rim, it produces slanting stripes. All of these are akin to the way chemical-wave patterns form.

A wasp (Vespula vulgaris) working on its nest. Why and how does it make the cells hexagonal? It seems clear that different types of wasp have different inherited instincts for their architectural designs, which can vary significantly from one species to another.

Butterflies (and sometimes even their caterpillar precursors) make inventive use of a small palette of pattern elements, such as eyespots, chevrons, stripes, and outlining of veins. These are arranged to suit many purposes—for example, warning to s deter predators, camouflage, mimicry, and species recognition.

Lava cracks. The final stages in the formation of the famous Giant’s Causeway in Ireland probably looked a bit like this—a crack network forming in the crust of molten lava. The islands here are rather more diverse in size and shape than the polygons of the Giant’s Causeway, but it’s thought that the crack network gradually reorganized itself as it penetrated deeper to become more regular. The irregular top layers were then removed by millions of years of erosion.

Logarithmic spirals such as this millipede body may be formed from the rolling up of a gently tapering cone.

A single layer or “raft” of bubbles contains mostly hexagonal bubbles, albeit not all of them perfect hexagons. There are some “defects”—bubbles with perhaps five or seven sides. Nonetheless, all the junctions of bubble walls are threefold, intersecting at angles that are close to 120 degrees.

The compound eyes of insects are packed hexagonally, just like the bubbles of a bubble raft—although, in fact, each facet is a lens connected to a long, thin retinal cell beneath. The structures that are formed by clusters of biological cells often have forms governed by much the same rules as foams and bubble rafts—for example, just three cell walls meet at any vertex.

Tiny parallel ridges on the surfaces of the scales of butterfly wings cause interference in the reflected light that picks out certain colors—in other words, some of these colors (particularly the iridescent blues and greens) are made not by light-absorbing pigments but by light-scattering structural patterns. However, even clear inspection of the wing scales of some butterfly species shows a still finer and more intricate structure.

When water sits on a water-repellent surface, it may break up into droplets. The shapes of these drops are governed by surface tension, which pulls them into roughly spherical shapes, as well as by gravity (which will flatten a droplet on a horizontal surface) and the forces that act between the water and the underlying surface. If those later forces are strong enough, the droplets are pulled into lens-shaped pancakes.

Branching crystals such as mineral dendrites, often mistaken for the fossils of ancient plants, can be very beautiful.