The Fractal Dimensions Of Attrctor Of Fractal Interpolation Functions

In recent years ,the study of fractal function has aroused wide concern .The fractal dimension of fractal function has been researched systematically .In this paper, the basic theories of fractal geometry are briefly proposed . We discuss the researches of fractal dimensions done by lots of scholars .After that ,we analyze the practical significance of the researches of fractal interpolation functions(FIF for short), and introduce the current situation of the studies of fractal interpolation curve and the fractal dimensions of the FIF.This article focus mainly on the Hausdorff dimension and Box dimension of the attractors of FIFs. Based on the previous studies, we give the estimates and proof for upper and low bounds of Hausdorff dimension of attractors of IFS. Then we construct the interpolation function system which generates the Weierstrass function. Based on this, we give the Box dimension. This method is the simplest we ever known. Then finaly, through the interpolation function system we get the upper bound estimate of Hausdorff dimension of the Weierstrass function.