The “fairy circles” of the Namib Desert exhibit strikingly regular spatial patterns, which have long mystified observers. (Jen Guyton)

No one is certain what causes the enigmatic “fairy circles” of the Namib Desert. The rings of burnt orange dirt, each impeccably round and enclosed in a fringe of tall, tufted grass, emerge suddenly from the spare landscape. Over the course of decades they expand — some become big enough to fit a school bus — then fade, as if they are creatures that live and die. So uniform is their distribution across hundreds of miles of desert that they seem to have been drawn by an alien hand.

The Himba tribespeople of northern Namibia, who have lived among the circles for centuries, say they are actually footprints laid down by gods who walked across the stark landscape at the beginning of time. Others — usually fanciful tour guides trying to pull one over on their customers — call them “dead spots” formed by the poisonous breath of a dragon that dwells beneath the earth.

Not even scientists can agree on an explanation. Some studies suggest that tiny insects shape the circles by munching at the grass above their nests. Other research indicates that they're a product of feedback systems among the clumps of grass — an example of plant self-organization.

“This is a classic thing in ecology where debates will emerge and go on for decades,” said Rob Pringle, an ecologist at Princeton University. “And the resolution after all that time is usually, 'Well, it's a little bit of both.' ”

That's the conclusion of a new paper Pringle and his colleagues published Wednesday in the journal Nature. Using computer models, the scientists demonstrated that the circles can emerge from complex interactions within and between termite colonies and the grass that grows around them. Their research explained not only the vast arrangement of the circles themselves — which mimics the hexagonal pattern of spots on a Chinese checkers board — but revealed the less noticeable centimeter-scale pattern of the grassy spaces between the circles.

The result doesn't definitively resolve the question of the fairy circles' origins — only experiments in the field can do that. But it does illustrate how order can emerge from chaos, and it offers hints at the strange geometry of the universe. It is a lesson in ecology, math and physics, written in sand by bugs and blades of grass.

Pringle didn't set out to solve the mystery of fairy circles. He works mostly in Kenya, studying the spatial patterning of termite mounds in the savanna. But he was intrigued by a 2013 survey of fairy circles in the journal Science reporting that sand termites live in almost all of them. That study's author, Norbert Juergens, suggested that the insects — which drink by pressing their mouths against moist grains of sand — might keep the round patches free of vegetation to ensure that rainwater sinks into the earth around their nests.

Not all researchers were convinced by Juergen's theory; many were skeptical that insects could be responsible for a pattern that propagates across hundreds of miles.

Graduate student Jen Guyton collects data on a fairy circle. (Tyler Coverdale)

Meanwhile, it emerged that the fairy circles in Namibia weren't the only ones in the world — almost the exact same phenomenon was reported in the Australian Outback in 2016.

The study of the Australian circles found no evidence of termites. But the phenomenon did match computer models for self-organization — a process by which random, small-scale interactions between individual entities produce an overarching order without any kind of central coordination. The theory, which has its roots with pioneering computer scientist Alan Turing, has been used to explain everything from the pattern of zebra stripes to the formation of crystals.

Proponents of the plant-organization hypothesis argue that vegetation can affect how scant rainfall sinks into the soil and then stays there. The growth of one clump of grass can encourage others, because the plant helps hold water and provides a small amount of protection from the blistering sun. Over time, the circles may emerge as the optimal way to distribute vegetation across a resource-poor landscape.

“That kind of gives this periodic pattern” said Corina Tarnita, a fellow Princeton ecologist and the lead author of the Nature paper. “This kind of theory can produce a suite of patterns depending on the availability of rainfall.”

Pringle and Tarnita, who has a mathematics background, thought there might be a way to reconcile the two theories. So they came up with a dynamic computer model that simulated both, taking into account factors such as rainfall and root growth. The system produced by their model looked just like the real fairy circles of the Australian and Namibian deserts.

What's more, the model revealed aspects of the circles that initially had been overlooked. It predicted that the grassy areas between the bare circles would also be organized into round clumps, distributed according to the same hexagonal pattern that characterizes the larger fairy circle arrangement.

Tarnita and Pringle were thrilled to see the photographs sent back by a colleague, Jen Guyton, who had traveled to Namibia to examine the circles up close. The images showed a flipped version of the overall pattern: circles of grass surrounded by dry, dusty earth.

“It's an amazing thing that you can get such clean, beautiful geometric patterns,” Tarnita said. “Such tiny creatures doing their thing very locally every day end up producing these unbelievable large-scale patterns. … To me, it's mind-boggling that nature can do that.”

But the new model revealed other surprises, too. Recently, Tarnita and Pringle sat down with Princeton chemistry professor Salvatore Torquato, who specializes in identifying the physics behind strange patterns in nature.

“The thing that immediately caught my eye about what they had was it seemed to fall into an exotic type of patterning I call hyperuniformity,” he said.

This phenomenon, which Torquato identified more than a decade ago, describes a type of arrangement that lies halfway between the extreme order of a crystal structure, where every atom is aligned predictably and perfectly with its neighbors, and the disorder of a liquid. If a crystal is like a Lego structure, solidly built according to set rules, and a liquid is like a bucket of Legos tossed out onto the floor, then hyperuniformity is what would happen if the Legos were strewn in such a way that order emerged from the overall mess. This happens at the atomic level, particularly in special kinds of matter called quasicrystals that have been produced in laboratories and discovered in meteorites. But it also has been found in the eyes of chickens, in soft-matter systems such as emulsions and in the large-scale structure of the universe.

And now, perhaps, in an ecosystem.

“You realize that you can find these patterns at many different scales,” Tarnita said. “Anywhere from tiny microbial colonies to animal coats to the scale of ecosystems. You find compelling patterns and, many times, the same kinds of patterns, the same motifs. ... It shows you how many ways nature has managed to come to the same conclusion.”

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