Scientists have studied trees depicted in various works of art and found they follow relatively simple mathematical rules ...

Put simply, “Fractals are defined as never-ending patterns that repeat the same basic shape at bigger and smaller scales.” Scientists, mathematicians and other experts have discovered fractals ...

This property, where the same geometric pattern appears at every scale within a shape (known as self-similarity), gives Romanesco cauliflower its remarkable "fractal" character. How have genetic ...

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

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 ...

This can then combine with two more to form a 54-monomer shape, which is again triangular and resembles a Sierpiński triangle ...

Marcus du Sautoy describes how fractal geometry can be used to describe natural objects, and how it is used in digital animation. Trees use the simple rule of trying to maximise surface area ...

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 ...