Two physicists from the University of Hokkaido in Sapporo, Japan, investigated a phenomenon that—come Christmas time—many young children observe every year. Looking out of the window they may notice icicles hanging from the roof gutters. The more curious among them may wonder about the ringlike ripples around the icicle, which occur at regular distances along its shaft. The two physicists had outgrown their childhood years but kept their curiosity. They could not help themselves but sit down and try to work out how the phenomenon comes about. The first thing they found was that the distance between two peaks always measures about 1 centimeter, independent of the length of the icicle and the outside temperature. The two scientists then developed a theoretical model that explains the surprisingly universal structure of icicles.

An icicle grows as thin sheets of water flow down its shaft. Part of the water freezes. The rest drips from the icicle’s tip. But the ice that is left behind does not build up uniformly. What the two physicists found was that two counteracting effects account for the mysterious ripple phenomenon.

The first effect is the so-called Laplace instability, which says that more ice builds up on the convex parts of the icicle’s surfaces than on the concave parts. This happens because protruding parts of the icicle are more exposed to the weather, and therefore more heat is lost there than from the somewhat protected indentations. This is why the ripples gradually grow thicker at these particular spots of the icicle. Another effect prevents these buildups from growing indefinitely, however. The Gibbs–Thomson effect says that the thin water layer that flows down the icicle’s shaft has a counterbalancing effect on the temperature, thus inhibiting a massive growth of the ripples.

With the help of no less than 114 equations the two researchers reached the conclusion that the peak-to-peak distance between the ripples must measure about 1 centimeter. Their analysis also yielded a prediction. The ripples should gradually migrate down the icicle at about half the speed that the icicle grows—a phenomenon the researchers hope will soon be verified experimentally.

The two Japanese physicists were not the first to be interested in hibernal phenomena. Four hundred years earlier the astronomer Johannes Kepler noticed that snowflakes always have hexagonal patterns, even though no two are ever alike. Pleased with his discovery, he set about writing a booklet that he presented the following New Year to a friend. In “A New Year’s Gift or On the Six-Cornered Snowflake,” Kepler attempted to explain the phenomenon. The learned scientist suggested several possible causes for the mysterious shape. At first he tried to find a relationship between the hexagonal shapes of ice crystals and honeycombs but was unsuccessful. Realizing that he did not have the means to answer his question, he finally gave up. In the closing words to his booklet he remarked that one day chemists would surely discover the true cause for the snowflakes’ sixfold symmetry. Kepler was right, but it took another 300 years, until the beginning of the 20th century, when the German scientist Max von Laue invented X-ray crystallography. Only with this new tool could the secret of the flakes’ crystal structure be made visible and explained.

Snow crystals form around dust particles that are swirled upward into the atmosphere. When they float back down in the humid air, water molecules attach themselves to the nucleus, that is, the dust particle. Like nearly everything in nature, the molecules attempt to attain the state of lowest energy. At temperatures between 12 and 16 degrees Celsius below freezing, this state is achieved when the water molecules are arranged in a lattice such that each molecule is surrounded by four others in a pyramid-like structure. Looking at the structure from above with the help of X-rays, it resembles a hexagon. The tips of the

hexagon branch out ever so slightly into space, but that suffices for what follows: water molecules, whirling around in the air, love to land on one of these protrusions. The tips, or snowflake arms, then keep growing, like dendrites, until even the naked eye can make them out. This is how snowflakes form.