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.

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 pattern or …

2 days ago · Over the last 50 years, fractals have challenged ideas about geometry and pushed math, science and technology into unexpected areas.

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.

Fractals have detail at arbitrarily small scales and display irregularity that cannot be described by traditional geometrical language. In other words, fractals are objects which, at any magnification, will …

Nov 7, 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 many irregularly shaped …

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.

A tutorial on basic fractal geometry and a panorama of uses of fractals, with supporting software, laboratory exercises, and resources for teachers

Fractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties. We’ll explore what that sentence means through the rest of the chapter.