A friend mine shared a gorgeous video show how coffee rings form at a microscopic level.

Apparently he found the video through a impressive blog called Empirical Zeal that’s maintained by a Physics grad student. The blog post, entitled “The Universal laws behind growth patterns, or what Tetris can teach us about coffee stains,” does a nice job of introducing the notion of universality classes and has several links to some excellent articles on recent mathematical advances in the field.

The mathematics centers on the KPZ (Kardar-Parisi-Zhang) equation, which is well-described in this expository mathematical article by Ivan Corwin: “The Kardar-Parisi-Zhang Equation and Universality Class.”