Natural Patterns

By Lawrence Wilkinson

“Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry”- Richard Feynman

More than 70 years ago, mathematician Alan Turing proposed a mechanism that explained how patterns could emerge from bland uniformity. As Amber Dance explains, scientists are still using his model — and adding new twists — to gain a deeper understanding of animal markings…

There’s a reason fashion designers look to animal prints for inspiration. Creatures have evolved a dizzying array of patterns: stripes, spots, diamonds, chevrons, hexagons and even mazelike designs. Some, like peacocks, want to be seen, to attract a mate or scare off a rival or predator. Others, like tigers or female ducks, need to blend in, either to sneak up on prey or to avoid becoming lunch themselves.

Some patterns arise simply or randomly, but others develop via complex, precise interactions of pattern-generating systems. Their beauty aside, the intricacies of these systems are inspiring the scientists who aim to elucidate how the tiger got its stripes, the cheetah its spots and more besides.

Mammals like cats and dogs can have white tummies. They get them in a straightforward way: As the embryo develops, pigment-making cells originate along the site of the future spine and migrate down and around toward the belly. But sometimes they don’t make it all the way. Where the pigment cells run out of steam, the white begins.

The black dots on Dalmatians are generated randomly. So are the black-and-orange splotches on calico cats.

But the stripes of chipmunks and tigers, the speckles on fishes and chickens, and many other glorious animal features are laid down with exquisite precision. In a remarkable feat of self-organization, a uniform surface becomes patterned.

The person who figured out how this happens was Alan Turing [here]. You may know him as the 20th century mathematician who broke Nazi codes during World War II and developed early concepts in artificial intelligence.Turing also turned his math skills to understanding how regular features could emerge on the developing embryo. Scientists since then have applied his equations to the development of such patterns as fingerprint ridges, the places where hairs will sprout, and color patterns like stripes and spots.And it turns out he was really onto something: Today, scientists studying animal patterns still find Turing’s ideas to be remarkably effective — especially when combined with other factors that elaborate the patterns further….

A colorful tour of what scientists are learning today, starting with Turing’s theory: “Spots, stripes and more: Working out the logic of animal patterns,” from @amberldance in @KnowableMag.

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(This has been just a glimpse, “a flake of your life” as Leonard Cohen said in “Famous Blue Raincoat.” Visit Mr. Wilkinson’s blog for more wonderful discoveries, like “A Horse! A Horse! My Kingdom for a Horse!“)