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 …

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 …

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 22, 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 …

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 …

In this section, we will introduce some of the fundamental ideas, and terminology that will help you begin to understand the mathematical principles that define fractals.

Discover what fractals are: infinitely complex patterns that repeat at every scale. Learn about fractal geometry, the Mandelbrot set, fractals in nature, math, AI, and more.