A quantum version of a fractal pattern, known as "Hofstadter's butterfly," has long been predicted, but the new study marks ...

After a nearly 40-year chase, physicists have found experimental proof for one of the first fractal patterns known to quantum physics: the Hofstadter butterfly. Named after Douglas Hofstadter ...

A fractal butterfly pattern produced by an unusual configuration of magnetic fields, first predicted almost 50 years ago, has been seen in detail for the first time in a twisted piece of graphene.

The Hofstadter butterfly is a fractal pattern—it contains shapes that repeat on smaller and smaller size scales. Fractals are common in classical systems such as fluid mechanics, but rare in the ...

First direct proof of Hofstadter butterfly fractal observed in moiré superlattices Date: May 15, 2013 Source: Columbia University Summary: Scientists have directly observed a rare quantum effect ...

This results in a quasi-continuous distribution of incommensurate quantum states with a self-similar recursive structure, yielding a butterfly-like fractal energy diagram called the Hofstadter ...