Researchers observed a long-predicted fractal energy pattern in twisted carbon materials, confirming quantum theories.

Trees depicted in famous artworks across a range of styles follow the same mathematical rules as their real-life counterparts, scientists have found. The math concept hidden in this tree art — ...

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 ...

A quantum version of a fractal pattern, known as "Hofstadter's butterfly," has long been predicted, but the new study marks the first time it has been directly observed experimentally in a real ...

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

The math concept hidden in this tree art — geometric shapes known as fractals — is apparent in branching patterns in nature and may be key to humans’ ability to recognize such artwork as ...

Ethereum could be on its way to similar 2017 gains as whales continue to buy ETH during the current market dip.

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.