Patterned ground

Why do stones on flat Arctic ground arrange themselves into circles and polygons with nobody sorting them?

A tundra flat, seen from a low aircraft, is tiled with rings of stone a few metres across, the coarse material heaped at the rims and the fine soil clean in the middles. It looks arranged. Nothing arranged it: there is no current, no wave, no animal, and on truly flat ground not even gravity has a preferred direction.

So the honest question is not "who sorted the stones" but "what asymmetry could a process with no direction possibly have?" Randomness alone produces mixture, not order. Something in the annual freezing must be one-way.

Begin with a single stone in wet, silty ground, and follow one winter. Water freezing in soil does not simply solidify in place; a freezing front draws unfrozen water toward itself through the thin films that persist on grain surfaces below zero, and grows discrete ice lenses. That is frost heave, and it is why a soil with a fine fraction lifts in winter while clean gravel does not.

Now the stone matters, because rock conducts heat better than wet soil. The freezing front reaches deeper beneath a stone than beside it, so ice grows under the stone and lifts it. Ask what happens on thaw. The ice melts, the stone should settle back — and it does not fully, because while the cavity was held open, fine material slumped and washed into it. The stone comes to rest slightly higher than it started.

Sit with that for a moment, because it is the whole trick. One cycle is nearly reversible; it is the infill that breaks the symmetry. Repeat it a few hundred times and stones migrate steadily upward while fines migrate down. That is why these grounds have a stone-free layer of fines under a coarse surface, and it explains vertical sorting completely.

But the puzzle was lateral. Why should stones gather into rims rather than carpet the surface evenly?

Here the argument is less settled, and I will flag it as such. The mechanism generally proposed is a feedback in the neighbourhood of each stone. Fine, frost-susceptible soil heaves; a patch already crowded with stones has little fine material and heaves less; heaving soil squeezes stones sideways, away from itself and toward the nearest stone-rich patch. A patch of stones therefore recruits more stones, and the fines it displaces make the neighbouring soil heave harder still. Any chance concentration grows. One influential numerical model (Kessler and Werner, recalled) reproduces circles, labyrinths and stripes from just two such interactions — lateral sorting plus squeezing — which is suggestive rather than proof.

What sets the size? The plausible constraint is the depth over which the freezing acts: the diameters, typically a few metres, are of the same order as seasonal frost penetration, which is what you would expect if the depth of the sorting layer sets the scale. The correspondence is loose, and I would not offer a formula.

Now the part that can be tested, and it is a good test because the prediction is sharp. If the pattern comes from an isotropic feedback, then on flat ground it must be isotropic — rings and nets. Add a slope and add something with a direction: soil creeping downhill. Creep should stretch the rings, and the fraction it wins should grow with gradient. So the whole family ought to lie on a single continuum: circles and nets where it is flat, elongated steps and garlands on gentle gradients, and clean downslope stripes where creep outruns lateral sorting. That continuum is what field surveys find, at transitions of only a few degrees.

The refuting observations follow immediately. Well-developed sorted circles sitting on a steep slope, or true stripes running across a genuinely flat flat, would break the account. So would patterns in ground that has no fine fraction at all, since without frost-susceptible material there is no heave to sort with — and clean gravel is indeed one of the settings where the ground stays blank.

One distinction is worth guarding. Not every polygon on the tundra is made this way. The large non-sorted polygons of ice-wedge country, tens of metres across, come from a different mechanism entirely: ground cracking in extreme winter cold, as any drying mud or cooling basalt cracks, with meltwater then freezing in the cracks. Same landscape, same word "polygon", unrelated physics — and the give-away is scale plus the absence of sorting.

The misconception hiding in the question is that order requires an orderer. What it requires is a bias plus repetition — here a fraction of a millimetre of infill per cycle, repeated for centuries.

It is worth separating the forcing from the feedback, because they explain different features. The forcing is the annual freeze cycle: external, periodic, and carrying no spatial information whatever — it cannot tell you why the rings are three metres across rather than thirty. Everything about the pattern's geometry comes from the feedback between neighbouring patches.

Finally, a caution about reading these forms as a climate signal. Sorted patterns take centuries to millennia to organise, so many of the ones mapped in mid-latitude uplands are relict, inherited from colder past conditions rather than active now. Presence proves the past; only repeat measurement of marked stones over decades shows whether a pattern is still moving.

• Why ice-wedge polygons crack on a thermal-contraction schedule, and what their degradation reveals about thawing permafrost.
• How cryosuction pulls liquid water toward a freezing front through films that persist well below zero.

Every term the collection defines is gathered in the glossary.