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.

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.

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 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.

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.

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 …

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 and …

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.

Nov 12, 2025 · Discover fractals—intricate patterns that repeat at different scales, shaping objects from snowflakes to galaxies. Learn about their relevance in our lives. Fractals are self-similar patterns with …