实际分形体维数计算中的不确定性

本文研究了实验中发现的一类实际分形体维数计算中的不确定性问题，指出产生其分维不确定性的根本原因在于实际分形体自相似结构的有限层次性，并且在理论上给子了证明.

THE UNCERTAINTY OF FRACTAL DIMENSION CALCULATION OF ACTUAL FRACTALS

The study of the uncertainty of fractal dimension is,the key to actual application of farctal theory.Lung et al. has reported the uncertainty of farctal dimension of perimeter area method used for fractal dissension calculation of actual fractals. We had studied the uncertainty of fractal dimension of capactity dimension equation used for study of the fractal structure of amorphous carbon thin film's cracks. and found that measurement yardstiks have the effect on fractal dimension in actual measurement. Based on the viewpoint of finite-level of actual fractals, measurement yardsticks are not arbitrary value, and are within the certain size range limited by actual fractal's structure ; going beyond the range, the obtained fractal dimension will be change and uncertain. We have interpreted the uncertainty of fractal dimension of capacity dimension equstion in fractal dimension calculation of actual fractals. Our method is universal and suitable for the analysis of other uncertainty of fractal dimension.