Is fractal art generative art?

Basic knowledge of fractal art and appreciation of works/tech/ graph/2006/3463.asp The world we humans live in is an extremely complex world, such as noisy urban life, unpredictable stock market changes, Complex life phenomena, winding coastlines, pitted ground, etc., all represent the particularly rich phenomena of the objective world. Various natural sciences based on traditional Euclidean geometry always imagine the research objects as regular shapes. However, the world we live in is so irregular and fragmented. Compared with Euclidean geometry, it has complete Different levels of complexity. Fractal geometry provides a new way to describe the order and structure in this irregular and complex phenomenon. 1. Fractal geometry and fractal art What is fractal geometry? In layman's terms, it is the study of geometry that is infinitely complex but has self-similar figures and structures in a certain sense. What is self-similarity? For example, there is no big difference in shape between a big tree and its branches and branches. The relationship between the big tree and its branches is called a self-similar relationship in terms of geometry; let’s take another leaf. , carefully observe the leaf veins, they also have this property; animals are no exception, the gene in a cell in a cow's body records all the growth information of the cow; and the surface of the mountain, no matter how you zoom in on its part , it's all so rough and unequal etc. These examples can be seen everywhere around us. Fractal geometry reveals the essence of the world. Fractal geometry is the geometry that truly describes nature. The word "fractal" is translated into English Fractal, which was coined by B.B. Mandelbrot, the founder of fractal geometry, in 1975 from the Latin word Frangere. The word itself has the characteristics of "broken", "irregular", etc. meaning. The highlight of Mandelbrot's research was his discovery in 1980 of the collection that bears his name, in which he discovered that the entire universe is self-similar in an unexpected way (see Figure 1). The boundaries of Mandelbrot set figures, with infinitely complex and elaborate structures. If the computer's precision were unlimited, you could enlarge her boundaries infinitely. Figures 2 and 3 are enlarged images of the two rectangular frame areas in Figure 1. As you zoom into an area, its structure changes, revealing new structural elements. This is just like the "winding section of coastline" mentioned earlier. No matter how you zoom in on its part, it is always winding and not smooth, that is, it is continuous and not differentiable. The smooth curves abstracted from calculus do not exist in our lives. Therefore, the Mandelbrot set is a challenge to traditional geometry. Using mathematical methods to color the enlarged areas, these areas become exquisite artistic patterns. These artistic patterns are called "fractal art". "Fractal art" is presented to people in a brand-new artistic style, making people realize that this art has the same aesthetic standards of harmony, symmetry and other characteristics as traditional art. What is worth mentioning here is the symmetry feature. The symmetry of fractals expresses the up and down, left and right and center symmetry of traditional geometry. At the same time, her self-similarity reveals a new symmetry, that is, the symmetry between the local part of the picture and the larger part, or the symmetry between the part and the whole. This symmetry is different from the symmetry of Euclidean geometry, but the symmetry of size ratio, that is, each element in the system reflects and contains the properties and information of the entire system. This is completely consistent with the example mentioned above: "The gene in one cell in a cow's body records all the growth information of the cow." No matter you look at it from a scientific point of view or an aesthetic point of view, she is so philosophical. She is an organic combination of scientific beauty and aesthetic beauty.