This paper discussed the refined box dimension of a family of fractal surfaces,the relationship between the refined box dimension of the star product fractal surface(SPFS) and the fractal curves defining the SPFS is obtained.

Since box dimension doesn t have countable stabilization, for all positive number s<n, where is a integer, we can find a countable compact set F of Rn whose box dimension equals to s.

An arithmetic for calculating box dimension of a time-sequence is put forward, and a gearbox is regarded as a typical device.

Using the quaternion expansion of the shifting number ,we determined the fractal structure of intersection of sierpinski footcloth with their translates, and set up the fundamental properties of Box dimensions of those intersection sets.

In accordance of the property of 2-value digital image,the principle and method of calculating SPFD adopting box-counting dimension were minutely discussed basing on the fractal theory.

Fractal properties of ultrasonic signal are researched based on normalized scale box-counting dimension method successfully.

The objective of this study is to analyzes the scale variation and the spatial patterns of Picea crassifolia populations in Qilian Mountains,using box-counting dimension,information dimension and correlation dimension,and to identify the relationships between the spatial pattern and some selected environmental factors.