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.

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.

5 days ago · 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 …

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 …

Apr 12, 2026 · 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 …

Fractals, as with all of mathematics, can be full of paradoxes- they can often be a source of creativity, beauty, and surprise- while at the same time they can be a powerful tool for analyzing and …

Nov 26, 2024 · In mathematics, a fractal is a mathematical set defined by its self-similarity, meaning its structure doesn’t change under magnification. Exact self-similarity only appears in purely …

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 repetitive features.

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.