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. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.

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.

Oct 31, 2023 · At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex. One of the earliest applications of fractals came about well before the use of the term.

Mar 28, 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 Hausdorff in 1918. Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth.

Aug 30, 2024 · 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-similarity. Fractals are typically created by repeating a simple process over and over in an ongoing feedback loop.

The meaning of FRACTAL is any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size. Did you know?

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, and triangles. Fractals have three basic types which are below. Now we explain all of them briefly.

Fractals are fundamental to understanding many chaotic systems, and have many applications in sciences. They are also beautiful and mesmerizing objects, as we have seen with the Mandelbrot and Julia sets. In this section, we collect examples of fractals in all scales in nature.

Sep 10, 2024 · Fractals are geometric figures, just like rectangles, circles and squares. But unlike those geometric figures, fractals have some special properties. Geometric objects, such as 2-dimensional figures, are similar if they have the same shape.

Apr 1, 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 scales, but the same "type" of structures must appear on all scales.