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Spheres with various mathematical patterns
Researchers at the Massachusetts Institute of Technology developed a mathematical equation that predicts how surface patterns form on curved objects. Pictured are spheres with various patterns including hexagon, labyrinthine and hexagonal dimples.
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When a grape slowly dries and shrivels, its surface creases, ultimately taking on the wrinkled form of a raisin. Similar patterns can be found on the surfaces of other dried materials, as well as in human fingerprints. While these patterns have long been observed in nature, and more recently in experiments, scientists have not been able to come up with a way to predict how such patterns arise in curved systems, such as microlenses.
Now, from their calculations, the MIT team has determined that one main parameter -- curvature -- determines the type of pattern that forms. Curvature is one major determinant of whether a wrinkling surface becomes covered in hexagons or a more labyrinthine pattern: The more curved an object, the more regular its wrinkled surface. The thickness of an object's shell also plays a role. If the outer layer is very thin compared to its curvature, an object's surface will likely be convoluted, similar to a fingerprint. If the shell is a bit thicker, the surface will form a more hexagonal pattern. The researchers say the theory may help to generally explain how fingerprints and wrinkles form.
The research was funded in part by the U.S. National Science Foundation.
Learn more about this research in the MIT news story Wrinkle predictions. (Date image taken: 2014; date originally posted to NSF Multimedia Gallery: Nov. 12, 2015)
Credit: Norbert Stoop
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