Have you ever wondered why some animals have spotted coats, while others have stripes, and still others have none? Scientists have dedicated countless hours to this question. One such scientist was the English mathematician, theoretical computer scientist, cryptographer, and philosopher Alan Turing. The secret lies hidden in the way embryos develop and how two substances diffuse into each other over time.
The Brilliant Mind of Alan Turing
There are truly brilliant minds. Alan Turing's is undoubtedly one of them. Best known for his work on breaking the secret code used by the German side during World War II and for his "Turing Machine", this English mathematician and computer scientist also took an interest in questions like the one in this article. We have all observed how colors are distributed on the fur of different animals. Some, like giraffes, have large colored spots. Others, like leopards, have small spots. A third group, which includes zebras, are covered in stripes. And some, the most "boring" ones, have all their hair in a single color. Yet almost no one stops to think about the reason for this variety of coats.
The Chemical Basis of Morphogenesis
In 1952, Alan Turing published a book titled "The chemical basis of morphogenesis" (also known as "The chemical bases of morphogenesis"). Why would a mathematician be attracted to these questions? Well, just as with Fibonacci numbers and many plants, animal spots are intimately related to mathematics. The first model of morphogenesis—one of the three fundamental aspects of developmental biology, along with the control of growth and cellular differentiation—was proposed by Turing and is known as "the reaction-diffusion model". Through a series of differential equations, the work describes the changes in concentration of two substances over time and how they diffuse and react with each other.
How Patterns Form on Animal Skin
When this model is applied to animals, it provides a satisfactory answer to questions such as: Why are some animals spotted with striped tails, but not the reverse? Why do certain animals have neither spots nor stripes? In vertebrates, skin color is determined by pigment-laden cells called chromatophores. These have a very particular origin: during the formation of the neural tube, the epithelial cells at the edges of the embryonic neural plate differentiate into migratory mesenchymal cells.
Some of these cells migrate beneath the embryonic ectoderm and eventually integrate into the epidermis. Depending on their development and accumulation of pigments, they will give the skin a lighter or darker tone. In short, the way two different chemical products react and are distributed in the animal's skin is what gives its fur color. One stimulates the production of melanin—the protein that gives skin its color—and the other blocks its production. Turing's model explains how the different coat patterns depend solely on the thickness and shape of the region where they develop. A single group of equations, more or less complex, serves to explain the design of the skin of all animals.
As the embryo develops in its mother's womb, the two chemical substances spread over its surface. Depending on the moment of development at which these changes occur, different patterns form. The shape and size of the skin regions impose limitations on the patterns that will appear on them. This explains why in an elongated shape—like a tail—spots transform into stripes.
These equations also allow us to explain the patterns on butterfly wings and the colored motifs of tropical fish. More recent studies indicate that the same equations could describe how the limbs of vertebrates form during their development.
A man who, only five or six years earlier, had deciphered the messages of the German Enigma machines also found the explanation for why animals have patterned spots. Isn't it surprising?
For more on the mathematics, see the reaction-diffusion system.
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