Fractal - Wikipedia
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. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set .
分形 - 维基百科，自由的百科全书
分形 （英語： fractal，源自 拉丁語： frāctus，有「零碎」、「破裂」之意），又稱 碎形 、 殘形，通常被定義為「一個粗糙或零碎的 幾何形狀，可以分成數個部分，且每一部分都（至少近似地）是整體縮小後的形狀」 [2]，即具有 自相似 的性質。 分形在数学中是一种抽象的物体，用于描述自然界中存在的事物。 人工分形通常在放大后能展现出相似的形状 [3]。 分形也被称为 扩展对称 或 展开对称。 如果在每次放大后，形状的重复是完全相同的，这被称为自相似。 自相似的一 …
What are Fractals? - Fractal Foundation
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. Geometrically, they exist in between our familiar dimensions.
Fractal | Mathematics, Nature & Art | Britannica
2024年12月6日 · 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
Fractals | Brilliant Math & Science Wiki
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 Geometry - Yale University
A tutorial on basic fractal geometry and a panorama of uses of fractals, with supporting software, laboratory exercises, and resources for teachers
Fractal -- from Wolfram MathWorld
2024年12月6日 · 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.
How Fractals Work - HowStuffWorks
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 in Math - Definition, Types, & Examples
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.
Fractals – Mathigon
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.