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.

Jul 23, 2025 · What Are Fractals? A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole. This property is known as self …

Jan 29, 2024 · Fractal geometry deals with complexity and irregularity. While on the other hand, traditional Euclidean geometry, deals primarily with simple shapes such as circles, squares, …

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

Feb 15, 2014 · The main goal of this paper is to provide a generalized definition of fractal dimension for any space equipped with a fractal structure. This novel theory generalizes the …

Nov 14, 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 …

Nov 26, 2024 · Imagine a shape so intricate that it reveals infinite complexity as you zoom in on a structure where patterns repeat endlessly at every scale. These mesmerizing forms, known as …

Jul 24, 2025 · A fractal is a never-ending, repeating pattern that appears similar at different scales. These intricate geometric structures are fundamental elements woven into the world …

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 …