ferns, and coastlines. The image shows a quantum version of a fractal pattern, known as “Hofstadter’s butterfly,” which has long been predicted, but the new study marks the first time it has ...

The complex shape of a fractal often gives an impression of the endless repetition of a pattern. Fern leaves, pine cones, romanesco broccoli, and succulent leaves are all examples of fractal.

Fractal patterns are found throughout nature on large, macroscopic scales, like in romanesco broccoli or fern plants, but ...