Data Post Processing Methods for Determination on Fractal Dimension

Abstract

Fractal dimension is a very important parameter in fractal theory. Usually fractal dimension is determined by the slop of log(Nr) versus log(1/r). In this paper, we focus on the effect of different data post processing method on fractal dimension. From original data of the fractal dimension determination, it can be seen that log(Nr) is positively related to log(1/r). For the low values of log(1/r), the slow change in log(Nr) in some small intervals is due to the slow change in the number of boxes covering every grid. Both the low scale and the high scale data have a significant effect on the fractal dimension, and the former contributes to a large fractal dimension while the latter contributes to a small one. To obtain an accurate fractal dimension, different data post processing methods are studied. Using the second power sample step is tried, which gives a uniform sample step in log(Nr) versus log(1/r) coordinate system, and weakens the effect of the low scale data. But the reserved points are too few to obtain an accurate fractal dimension, which is a statistic quantity. At last, the three-line fitting is tried, the fractal dimension is determined by the slope of middle line, which eliminates the effect of low and high scale data, and gives a reasonable and optimization result.