Mathematical multifractal theory is a method to study complex structures, which can be used to describe many phenomena in nature. Here are some applications:

1. Seismology: When seismic waves propagate underground, they will be reflected and refracted many times, forming a complex path. Multifractal theory can be used to describe the distribution characteristics of these paths, so as to better understand the propagation law of seismic waves.

2. Geology: The pore structures in rocks are very complex, and the distribution characteristics of these pore structures can be described by multifractal theory, so as to better understand the properties of rocks.

3. Biology: The morphology and structure of organisms are very complex, and the multifractal theory can be used to describe the distribution characteristics of these morphology and structure, so as to better understand the growth and development law of organisms.

4. Physics: The molecular arrangements in liquids and gases are very complex, and the multifractal theory can be used to describe the distribution characteristics of these molecular arrangements, so as to better understand the properties of liquids and gases.

5. Computer science: Image segmentation and classification are often needed in image processing, and multifractal theory can be used to describe the boundary distribution characteristics of different regions in the image, so as to better realize image segmentation and classification.