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Physics

Physicists capture a strange fractal ‘butterfly’ for the first time

The electrons in a twisted piece of graphene show a strange repeating pattern first predicted in 1976, but never directly measured until now

By Alex Wilkins

26 February 2025

Theoretical calculation of the energy levels of electrons in twisted layers of graphene in a magnetic field, showing the fractal “butterfly” pattern predicted by Douglas Hofstadter

Yazdani Lab, Princeton University

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.

While a physics student in 1976, the computer scientist Douglas Hofstadter predicted that when certain two-dimensional crystals were placed in magnetic fields, their electrons’ energy levels should produce a strange pattern that looks the same no…

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