In a discovery that brings a legendary quantum theory to life, physicists at Princeton University have directly observed ...

These allowed energy levels (black dots) form a rare example of a quantum fractal known as "Hofstadter's butterfly", which shows self-repeating features on different scales. This plot shows how ...

Fractals are self-repeating patterns that occur on different length scales and can be seen in nature in a variety of settings, including snowflakes, ferns, and coastlines.