Abstract: At present, fractal has been involved in many fields of science and life. Because the matter with fractal characteristics may have some special properties and functions, scientists are urged to study the physical and mathematical mechanisms of fractal, explore some hidden laws in disordered systems, and use fractal dimension values to order disordered systems. [Keywords:] Fractal self-similarity Fractal theory, dissipative structure theory and chaos theory are considered as the three major scientific discoveries in 1970s. 1967, B. B. Mandelbort of Mandelbort published an article entitled "How long is the coastline of Britain? In the authoritative American magazine Science. A famous newspaper. It is pointed out that the coastline has self-similarity in morphology, that is, the regional morphology is similar to the overall morphology. In fact, forms with self-similarity exist widely in nature and social life. Mandelbrot called these forms similar to the whole to some extent fractal. On this basis, the science of studying fractal properties and its application is formed, that is, fractal theory, self-similarity principle and iterative generation principle are important principles of fractal theory. Due to the particularity of fractal theory research and its wide application in nature, fractal theory has quickly become a powerful tool to describe and deal with irregular graphics after unbalanced and nonlinear effects appear in nature and engineering. Since the development of fractal theory, a lot of theoretical and practical work has been carried out on the application of fractal theory in various aspects and materials science at home and abroad. At present, classification theory has penetrated into all fields of materials science, especially polymer materials. The application of fractal theory in polymer materials science is discussed below. 1. The methods of measuring fractal dimension can be roughly divided into the following five categories according to the different research objects: changing the observation scale to find the dimension; Calculate the dimension according to the observation degree relationship; Find the dimension according to the correlation function; Calculating the dimension according to the distribution function; According to the spectrum, when fractal is applied to material science, the commonly used methods to determine fractal dimension are box dimension method, code scale method and island method. Second, the study of fractal theory in polymer structure-the fractal in polymer chain structure is constantly changing with the conformation of the chain, so the treatment of this kind of problem belongs to "random flight" in statistical mathematics. However, from the fractal point of view, polymers have obvious fractal characteristics and can be tracked and monitored. The same is true of self-avoiding walking, which is common in polymers, but shows different fractal behaviors. Because such problems are similar to critical phenomena, we can also use powerful tools such as renormalization group. Another unique function of fractal dimension is that it can sensitively reflect the single conformation of a single polymer [4]. Due to the existence of macromolecular chains in polymer solution, the fractal in polymer solution is different from ordinary liquid in many aspects, such as rheological behavior and stress transfer that ordinary liquid does not have. In practical research. Fractal structure mainly exists in the gelation reaction of polymer solution. The gelation reaction of polymer solution mainly refers to the gelation process of polymer, which is a critical phenomenon and a semi-condensed state between crystalline and amorphous. In this process, polymer chains will form a network structure, which is a complex system with random, disordered and irregular shapes. However, the system is a gelation reaction that can be studied by fractal method, and there is self-similarity at submicroscopic level. For example, in the styrene divination reaction studied by Zuo Yi, the fractal in solid polymers for polymer materials, when the solid polymer materials break, materials with different mechanical properties will form different cross-sectional shapes, which are generally irregular and approximate or statistical fractal structures, which can be analyzed and characterized by fractal theory, so as to quantitatively evaluate the mechanical efficiency of materials according to the cross-sectional shapes. However, due to a large number of tiny holes distributed in microporous materials, these micropores have irregular microstructure, which makes the microporous materials present complex morphology both in the whole and in the region, which can not be described by traditional geometric theory, and the complexity of micropore morphology can be quantitatively characterized by fractal geometry theory [5]. Fractal in tetragonal polymers can be seen from dilute solution, viscoelastic crystallization and oriented crystallization of polymers. Only by crystallizing from a dilute solution can a flaky single crystal with regular folding near the molecular chain be obtained. Crystallization from melt cooling or heating from glassy state generally produces spherulite polycrystalline aggregates piled up by many platelets, and spherulites contain many amorphous regions. Of course, the crystallization of polymer is very imperfect, even single crystal has many defects, such as dislocation of chain end, holes, uneven folding surface and so on. Because of the complexity of polymer crystallization, it is not realistic to describe its morphology with Euclidean geometry, but if the randomly arranged segments are under certain conditions. When it is rearranged into an ordered structure, it can be described by fractal theory. Since the concept of fractal was put forward, it has been widely introduced into many disciplines and fields. The same application in polymer materials is also very important. Through computer simulation, several fractal aggregation models are established, which provides a powerful means for the application of fractal in polymer materials. At present, the application of fractal theory in the scientific research of polymer materials still has great potential and needs further study by workers from all over the world.