In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension.

Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.

Dec 20, 2025 · Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth. They are capable of describing …

So, you might be asking what exactly is a fractal? Well, a fractal, by definition, is a curve or geometric figure, each part of which has the same statistical character as the whole.

Oct 31, 2023 · You can create fractals with mathematical equations and algorithms, but there are also fractals in nature. At their most basic, fractals are a visual expression of a repeating …

Aug 19, 2025 · But fractals are more than just a subfield of math. Their characteristic roughness helps scientists visualize chaos and model the evolution of changing systems.

Jul 23, 2025 · Fractals represent complex mathematical objects that have been extensively studied as well as depicted by mathematicians, artists, and scientists because of their …

May 12, 2016 · Learn what a fractal is and what fractals are good for. See examples of natural fractals and artwork made using mathematical equations.

Dec 3, 2025 · A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but …

Fractals contain patterns at every level of magnification, and they can be created by repeating a procedure or iterating an equation infinitely many times. They are some of the most beautiful …