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The stripes looked like a mistake.

Several years ago, a team of physicists at Stanford University led by Aharon Kapitulnik was trying to grow a thin layer of bismuth crystal on a metallic surface. But instead of forming a uniform sheet, the crystal became a patchwork of uneven growth. In some areas — those where the crystal layer was only one atom thick — a striking design emerged. Small stripes filled up irregular patches, and these regions butted against one another, their stripes oriented at different angles.

Kapitulnik couldn’t explain the stripes. Then on a working trip to Paris in 2017, he showed them to Yuki Fuseya, a theorist at the University of Electro-Communications in Chofu, Japan. “This is like a zebra,” Fuseya told Kapitulnik. And if the stripes were really like a zebra’s, he said, they could be a Turing pattern.

The possibility came as a surprise. Countless patterns in nature, from zebra stripes to psychedelic hallucinations and windswept ripples in sand, are thought to stem from a mechanism that Alan Turing proposed in 1952, between his famed code-breaking work during World War II and his tragic death in 1954. This kind of pattern has since been identified in the arrangement of bacteria, stripes on sea shells, and even the distribution of human settlements. This ever-growing list includes systems on vastly different scales, from embryos to galaxies.

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