Papers by Keyword: Box-Counting Dimension

Abstract: This paper used three kinds of fractal dimensions to characterize spatial structure of the urban system in Shenyang Economic Zone, namely aggregation dimension, spatial correlation dimension, and box-counting dimension. It was found that the spatial structure of the Shenyang Economic Zone urban system has obvious fractal properties. In analysing the results of our research the following conclusions emerged: The space distribution of the Shenyang Economic Zone urban system is centripetal gathered around the central city of Shenyang, the accessibility of the transport network between cities is good, and the spatial shape is more compact than other urban systems of Liaoning Province. The authors believe that the structure of the Shenyang Economic Zone urban system is more effective than the structure of Liaoning Province urban system, and put forward rationalization proposals to optimize the urban system of the Shenyang Economic Zone.

Abstract: The roots can significantly increase the soil reinforcement of vegetation, and the fractal theory provides a new perspective for vegetation roots studies. This article applied the Fractal Fox software to calculate the fractal dimension of medicago sativa and cynodon dactylon roots in different growth periods and proved that the two species show fractal characteristics. The conclusions from the analysis are as follows: ①The fractal dimensions of the two plant roots tend to be stable with the increase of growth period; ②The fractal characteristic value of cynodon dactylon root is more significant than medicago sativa root; ③Compared with medicago sativa root, cynodon dactylon root is more effective in increasing the shear strength of soil.

Abstract: From the perspective of fractal geometry, the irregularity and complexity of near-fault ground motions and seismic responses of single degree of freedom (SDOF) are analyzed. Based on the box-counting method, the fractal dimensions of 30 acceleration time series of near-fault ground motions from Taiwan Chi-Chi earthquake and California Northridge earthquake are calculated. It is indicated that the acceleration time series of ground motions present the statistical fractal property, and the influence of characteristics of near-fault ground motions on their box dimensions is remarkable. Moreover, the box dimensions of ground motions reflect their frequency property to a large extent, and can be regarded as alternative index to represent their frequency content. Finally, for the time histories of seismic dynamic responses of elastic and inelastic SDOF systems subjected to near-fault ground motions, their box dimensions are computed to examine the fractal property.

Abstract: In this paper, we analyze the stock of Nanjing Panda Electronics Co Ltd for the 44-year period, from May 2, 1996, to October 9, 2009, a total of 3200 trading days. Using the Box-counting dimension method, we find that the financial data have different power law exponents in the plot for the number of box and diameter of box, which indicates the multifractality exist in the time series. In order to investigate the latent properties in the data, the width and maximum of the singular spectrum are calculated. The results show the strong degree of multifractality in the time series.