Penguin math

During harsh Antarctic winters, temperatures can drop to minus 40 degrees Fahrenheit with winds up to 87 miles per hour. To stay warm, emperor penguins squeeze together in compact huddles that can include thousands of birds. But it turns out they don’t bunch together randomly.

Researchers at Cornell University in Ithaca, N.Y., recently published a research paper showing the penguins huddle in a way that protects each individual within the colony and efficiently transfers body heat from one bird to another.

Penguins may not know anything about math, but their formations align with sophisticated physics and geometry concepts. The research validates an earlier study in which a team of researchers with the Woods Hole Oceanographic Institution used robotic, high-resolution cameras at a remote Antarctic research station to monitor the penguins’ behavior and measure the movements of individuals within the colony.

“A penguin huddle looks like organized chaos,” François Blanchette, a mathematician at the University of California, Merced, told Quanta Magazine.

But chaos it is not. The penguins systematically move so each one spends time at the center of the cluster, which can reach 100 degrees Fahrenheit. The birds on the frigid windward side quickly move to the more comfortable leeward side. They push the leeward penguins to the middle, and the center penguins move out to the windward edge of the huddle. Over a few hours, the penguins cycle through these rotations multiple times so each bird gets several chances to warm up in the middle.

The Cornell researchers used mathematical models that incorporated more data about how the penguins generate and transfer body heat in a huddle. What they found astonished them even more. Huddles start off as misshapen blobs. But as more individual penguins shift away from the windy side, the boundary of the pack begins to form a hexagon. Within that shape, each penguin lines up as though it was on a hexagonal grid or honeycomb. The formation allows for the densest packing and optimum arrangement for sharing warmth.

When the scientists calculated what the temperature would feel like to the penguins accounting for humidity, wind speed, and solar radiation, their movements were so mathematically precise that the team could use the data to accurately predict how individual penguins within the huddle would maneuver. Blanchette noted that the birds, without knowing it, formed into an almost perfect arrangement: “We tried to think of a better way [penguins could huddle], but it always involved an omniscient being who would tell them where to go.”