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

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 ...

A quantum version of a fractal pattern, known as "Hofstadter's butterfly," has long been predicted, but the new study marks the first time it has been directly observed experimentally in a real ...

The detailed observations of a butterfly enthusiast helped Montana ... by Harlan Radcliff over 17 years to analyze how ...