Fractal - Wikipedia
网页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.
What are Fractals? - Fractal Foundation
网页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.
How Fractals Work - HowStuffWorks
网页2023年10月31日 · 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 pattern or formula that starts out simple and gets progressively more complex.
Fractals | Brilliant Math & Science Wiki
网页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.
Fractal | Mathematics, Nature & Art | Britannica
网页2024年8月15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 – Mathigon
网页In mathematics, we call this property self-similarity, and shapes that have it are called fractals. They are some of the most beautiful and most bizarre objects in all of mathematics. To create our own fractals, we have to start with a simple pattern and then repeat it over and over again, at smaller scales.
What are fractals and how can they help us understand the world?
网页2024年5月21日 · Formally speaking, fractals are infinitely complex patterns that are self-similar across different scales. But, in an echo of their geometry, fractals can help us better understand the world on...
7.4: Fractals - Mathematics LibreTexts
网页2020年9月12日 · Fractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties. We’ll explore what that sentence means through the rest of this section. For now, we can begin with the idea of self-similarity, a characteristic of most fractals.
Fractals in Math - Definition, Types, & Examples
网页2024年1月29日 · Fractal is a pattern that never ends. It elaborates mathematical constructs that exhibit self-similarity, meaning they display similar patterns or structures when zoomed in or out. This self-similarity occurs at many levels of magnification, revealing elaborate details that are replicated at every scale.
Fractal -- from Wolfram MathWorld
网页4 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.