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.

Sep 10, 2025 · Fractal, in mathematics, any of a class of complex geometric shapes that commonly have “fractional dimension,” a concept first introduced by the mathematician Felix …

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.

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, …

Jul 23, 2025 · In mathematics, fractals are often defined using recursive algorithms and can have a non-integer dimension, known as a fractal dimension, which differentiates them from …

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 24, 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 …

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

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 …

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.