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> Keeping warm by huddling is the Emperor's trick, and it follows  a math pattern, but the birds don't do math, they constantly shift to find the warmest spot:
> 
> http://abstractions.nautil.us/article/604/math-of-the-penguins?mc_cid=52cd39af09&mc_eid=6d09ed0f17
> 
> “'A penguin huddle looks like organized chaos,” said François Blanchette, a  mathematician at the University of California, Merced. “Every penguin acts individually, but the end result is an equitable heat distribution for the whole community.”
> 
> "It turns out that penguins execute their huddles with a high degree of mathematical efficiency, as Blanchette and his team discovered. 
> 
> ***
> 
> "Though dominant winds can appear to push a huddle along the ice, the truth is more nuanced. Blanchette and his team’s model made clear that the birds do not move in unison. Penguins in the huddle’s center, where temperatures reach a sweltering 100 degrees Fahrenheit, mostly stand still. A bird who finds himself on the huddle’s windward side is soon driven to relocate to its warmer, leeward side. As more birds leave the windward side, penguins in the center soon find themselves exposed. In due course, these penguins also depart for the leeward side. 
> 
> "Huddles typically last a few hours, during which the penguins may cycle through multiple rotations from the huddle’s cold exterior to its warm interior. In the process, each individual prioritizes his own warmth, yet the huddle’s heat is shared by all. 
> 
> ***
> 
> "Penguins seem to know what mathematicians learned long ago: The densest packing of shapes on a plane is a hexagonal grid. According to Blanchette’s model, the birds arrange themselves as if they were each standing on their own hexagon in a grid. Most huddles start off as misshapen blobs. Wind flow and temperature around the huddle prompt a first penguin—typically the coldest on the windward side—to relocate. This penguin, known as the mover, waddles in search of new neighbors in the relative warmth of the huddle’s leeward side."
> 
> Comment: The diagrams are a must-see to fully understand. The math is pure human observation math. Penguins don't understand the packing trick of hexagons. They have learned how to keep warm.