A Family Of Fractal Surfaces And Their Dimensions

Fractal is a useful tool in studying complexity geometry objects; it has a great function in many fields. By the studying of the fractal surfaces' dimension, we own a great means in researching the objects in the nature and practices.In this paper, we introduced the dimension theory and the product theory in fractal. Pointed out that we can acquire a fractal surface with roughness in one fragment by the fractal product,. Introduced the Star Product Surface (SPS), Fractal interpolation function (FIF) and their box dimension. Defined the refined box dimension of the SPS, found out the relations of the relationship between the refined box dimension of the SPS and the fractal curves defining the SPS is obtained. We discussed how to obtain the SPS by the FIF. Further more, discussed the box dimension of the SPS in different fragments, gave the relation of the box dimensions between the profile curves of SPS and the curves used for constructing the SPS is obtained. The SPS have the roughness in every direction; can. simulate the rough and irregular abnormity surfaces in the nature. By the further studying in this paper, it supplied the theory foundation for applying fractal in practices.