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Researchers have worked a way to predict how everything from a face to a raisin will wrinkle.

They say their algorithm can accurately predict wrinkles on a curved surface for the first time.

They say it helps explain how our fingerprints, and wrinkles on our face, form over time.

A team of MIT mathematicians and engineers has developed a mathematical theory, confirmed through experiments, that predicts how wrinkles on curved surfaces take shape - even on skin.

As 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.  

'If you look at skin, there's a harder layer of tissue, and underneath is a softer layer, and you see these wrinkling patterns that make fingerprints,' says Jörn Dunkel, an assistant professor of mathematics at MIT. 

'Could you, in principle, predict these patterns? It's a complicated system, but there seems to be something generic going on, because you see very similar patterns over a huge range of scales.'

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.

Theteam of MIT mathematicians and engineers has developed a mathematical theory, confirmed through experiments, that predicts how wrinkles on curved surfaces take shape.

From their calculations, they determined that one main parameter — curvature — rules the type of pattern that forms: The more curved a surface is, the more its surface patterns resemble a crystal-like lattice.

The researchers say the theory, reported this week in the journal Nature Materials, may help to generally explain how fingerprints and wrinkles form. 

In past experiments, Reis manufactured ping pong-sized balls of polymer in order to investigate how their surface patterns may affect a sphere's drag, or resistance to air.

The group sought to develop a general theory to describe how wrinkles on curved objects form — a goal that was initially inspired by observations made by Dunkel's collaborator, Pedro Reis, the Gilbert W. Winslow Career Development Associate Professor in Civil Engineering.

In past experiments, Reis manufactured ping pong-sized balls of polymer in order to investigate how their surface patterns may affect a sphere's drag, or resistance to air. 

Reis observed a characteristic transition of surface patterns as air was slowly sucked out: As the sphere's surface became compressed, it began to dimple, forming a pattern of regular hexagons before giving way to a more convoluted, labyrinthine configuration, similar to fingerprints.

'Existing theories could not explain why we were seeing these completely different patterns,' Reis says. 

In computer simulations, the researchers confirmed that their equation was indeed able to reproduce correctly the surface patterns observed in experiments. 

They were therefore also able to identify the main parameters that govern surface patterning.

As it turns out, 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.