A team of scientists from Princeton University has measured the energies of electrons in a new class of quantum materials and has found them to follow a fractal pattern. Fractals are self-repeating ...

In a discovery that brings a legendary quantum theory to life, physicists at Princeton University have directly observed Hofstadter’s butterfly — a fractal pattern in electron energy levels that was ...

Almost 50 years ago, computer scientist Douglas Hofstadter predicted that a butterfly would spread its wings in the quantum world. Under the right conditions, tiny electrons in a quantum system could ...

Fractal geometry investigates complex shapes that exhibit self-similarity across multiple scales, while spectral analysis focuses on the study of the eigenvalues and eigenfunctions of operators, most ...