中文摘要：

主要从分形插值函数的理论出发，利用Matlab软件绘制分形插值函数的图像，绘出确定的垂直压缩因子与随机垂直压缩因子的函数图像，定性地分析垂直压缩因子的变化所引起的分形插值函数图像的变化．最后，通过计算得到分形插值函数的图像的盒维数随着垂直压缩因子的变大而变大．

英文摘要：

Based on the theories of fractal interpolation functions, by using Matlab software, we draw the images of fractal interpolation functions for the determined vertical compression factors and random vertical compression factors. Quantitatively analyze the change of the images of the fractal interpolation functions caused by the vertical compression factors. Finally, we calculate Box dimension of the fractal interpolation function. Therefore, the relationships between the vertical compression factors and Box dimensions of fractal interpolation functions are obtained.