Fractal generally refers to "a rough or fragmentary geometric shape, which can be divided into several parts, and each part (at least rough) is a whole reduced size shape", which is called self-similarity. Mandebo put it forward in 1975, which means "fragmentary" and "broken". Fractal generally has the following characteristics: it can have fine structure on any small scale; It is so irregular that it is difficult to describe it in the language of traditional Euclidean geometry. The Hausdorff dimension of self-similarity (at least roughly or arbitrarily) will be larger than the topological dimension (except in curves full of space such as Hilbert curves); There is a simple recursive definition.

Because fractals are similar on all scales, they are usually considered infinitely complex (in imprecise terms). Things similar to fractals in nature include clouds, mountains, lightning, coastlines and snowflakes. However, not all self-similar things are fractal. Although the solid line is self-similar in form, it does not conform to other characteristics of fractal.

/kloc-in the 7th century, the mathematician and philosopher Leibniz thought about recursive self-similarity, and fractal mathematics gradually took shape (although he mistakenly thought that only straight lines would be self-similar).

Until 1872, Karl Veiershtrass gave a function that is continuous but differentiable everywhere. Today, it is considered as a fractal graph. 1904, Koch van Kaka was dissatisfied with Weiher's abstract and analytical definition, and gave a definition with similar function but more geometric significance, which is today's Koch snowflake. The following year, the Scherbinsky carpet was made.1904. At first, these geometric fractals were considered as fractals, and ...10086.00000000000606 1938 Paul Pierre Lé vy further put forward the concept of self-similar curve in his paper "Curves and Surfaces in Plane or Space Composed of Parts Similar to the Whole", in which he described a new fractal curve-Levi's C-shaped curve.

Georg Cantor also gave a subset of real numbers with unusual properties-Cantor set, which is also considered as fractal today.

Iterative functions of complex plane were studied by Jules Henri Poincare, Felix Klein, Pierre Fatu and gaston Joulia in the end of 65438+2009 and the beginning of the 20th century, but until now, many functions they found showed their beauty with the help of computer drawing.

The "fractal fever" that began in the early 1980s lasted for a long time. As a new concept and method, fractal is being applied in many fields. John wheeler, an American physicist, said: Whoever is not familiar with fractals in the future cannot be called scientific literacy. This shows the importance of fractal. Professor Zhou Haizhong, a famous scholar in China, believes that fractal geometry not only shows the beauty of mathematics, but also reveals the essence of the world and changes the way people understand the mysteries of nature. It can be said that fractal geometry is a kind of geometry that truly describes nature, and the research on it has greatly expanded the cognitive field of human beings. As a very popular and active new theory and discipline in today's world, fractal geometry makes people re-examine the world: the world is nonlinear and fractals are everywhere. Fractal geometry not only makes people realize the integration of science and art, the unity of mathematics and artistic aesthetics, but also has its profound scientific methodology significance.