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

2023年10月31日 · 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.

2025年3月28日 · 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 objects or spatially nonuniform phenomena in nature such as coastlines and mountain ranges.

FRACTALS is an interdisciplinary journal on complex geometry, patterns and scaling. Covers recent developments in complex spatial and temporal behaviors in both nature and society.

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.

2024年1月29日 · 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.

2024年5月30日 · Take a tour through the magical world of natural fractals and discover the complex patterns of succulents, rivers, leaf veins, crystals, and more.

fractal is a geometric shape that has a fractional dimension. Many famous fractals are self-similar, which means that they consist of smaller copies of themselves. Fractals contain patterns at every level of magnification, and they can be created by repeating a procedure or iterating an equation infinitely many times.

5 天之前 · 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.