Fractal diagram of fractal diagram

When people talk about fractals, they often have two meanings.

First, what is its actual background? Second, what is its exact definition?

Mathematicians study fractals in an attempt to use mathematical methods to simulate various seemingly irregular phenomena that exist in nature and appear in scientific research. In the past few decades, fractals have been widely used or paid close attention to in physics, materials science, geological exploration, and even stock price prediction, and due to the introduction of fractals, some disciplines have gained new vitality. . What is called fractal in mathematics is abstract. And those specific objects in nature that people think of as fractals are not what mathematicians call fractals, but approximations at different levels.

In 1985, Mandelbrot won the Barnard Medal. This award is specially awarded to those who have made significant contributions and influential figures in the physical sciences or other natural sciences. In the list of winners every five years, there are a group of world-renowned scientists such as Einstein and Fermi, which shows the scientific status and influence of Mandelbrot's fractal research. In 1995, at the invitation of the Chinese scientific community, Mandelbrot visited China and gave a lecture.

Fractal graphics are very different from common engineering drawings. Fractal graphics generally have self-similarity. This means that if you continuously enlarge and observe parts of the fractal graphics, you will find fine structures. , more fine structures will appear again, which can be said to be endless and never-ending. The artist paints different colors on different areas of the fractal picture, and what appears in front of us will be a very beautiful picture.

Almost at the same time that Mandelbrot won the Barnard Medal, represented by mathematicians and computer experts H. Peotgen and P. Richter from the University of Bremen in Germany, the most advanced computer graphics at the time A large number of fractal patterns were produced on the workstation; J. Hubbard and others also completed a computer animation called "Chaos". Then, albums, calendars, postcards, and even T-shirts printed with fractals were released one after another. Starting in the mid-1980s, first in Western developed countries and then in China, fractals gradually became a popular vocabulary, and even teenage children became fascinated by fractal games on computers. The Computer Graphics Group of North China University of Technology in Beijing completed a computer animation film "Similar" in 1992. This film focused on the similarity of fractal graphics. It was also the first film completed using computer digital technology in my country. Won the Science and Technology Progress Award from the Ministry of Film and Television that year.

More people are intoxicated with fractals, not because of science, but because of the beauty of fractals. The aesthetics of mathematics are difficult for ordinary people to understand: How can a large number of numbers, formulas, and symbols be reflected? However, computers can intuitively present some of the inherent beauty of mathematics and give it formal expression. As a type of illustration, fractals provide a wonderful annotation for the beauty contained in mathematical theory and practice. It fully reflects the connotation of simplicity, harmony and unity in mathematical science!

On the one hand, artistic creations that never take scientific content as the theme themselves also quote a lot of scientific terms such as "dynamic system", "iterative approximation", "chaotic attractor", etc., and then try their best to use computer graphics methods , creating incredibly magical works. From this point of view, it can be said that artists have begun to wander into the realm of science!

On the other hand, scientific books that always face readers with a serious expression are uncharacteristically, and their titles have become romantic: "The Beauty of Fractals" (1986), "Fractals Everywhere" (Fractals Everywhere) Visible), "The Algorithmic Beauty of Plants" (1990), .... A large number of exquisite scientific wall charts showing fractals, disguised, appeared in the exhibition hall of the art museum, accepting the comments of art connoisseurs, scientists From then on, he entered the sacred palace of art!

The beauty of fractals often requires computer processing to be expressed. Today, people can browse and appreciate various fractal works of different styles on the Internet, some of which are aimed at special objects to be expressed in scientific research, and some are completely artistic. The Internet world will provide you with many wonderful and surprising fractal pictures, which will make you feel refreshed and sometimes dazzled.