Ernie Button, a photographer in Phoenix, found art at the bottom of a whisky glass. Howard A. Stone, a mechanical and aerospace engineering professor at Princeton, found the science in the art.

Eight years ago, Mr. Button was about to wash the glass when he noticed that leftover drops of Scotch had dried into a chalky but unexpectedly beautiful film. “When I lifted it up to the light, I noticed these really delicate, fine lines on the bottom,” he recalled, “and being a photographer for a number of years before this, I’m like, ‘Hmm, there’s something to this.’ ”

He and his wife began experimenting. The Scotches with smoky, peaty flavors, like those from the islands of Islay and Skye in western Scotland, were inconsistent, needing more trial and error to produce the picturesque ring patterns. By contrast, those from the valley around the River Spey in northeastern Scotland “seem like they’ll work every time,” Mr. Button said.