'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.