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

A quantum version of a fractal pattern, known as "Hofstadter's butterfly," has long been predicted ... which involved stacking and twisting two sheets of carbon atoms to create a pattern of ...

Scientists at Princeton University have made a groundbreaking discovery in quantum materials, revealing that electron energy levels in certain systems follow a fractal pattern known as Hofstadter’s ...