In a first, physicists have directly seen Hofstadter’s butterfly—a long-sought-after fractal in the quantum realm ...

In a discovery that brings a legendary quantum theory to life, physicists at Princeton University have directly observed Hofstadter’s butterfly — a fractal pattern in electron energy levels that was ...

Mahomet-Seymour sixth-grade students, from left, Nate Nelson, Ethan O’Malley, Brody Melchoirre and Izzy Empson connect to a scanning electron microscope ... seeing a butterfly wing in minute ...