Information dimension

General properties of fractals

Published in Xie Heping, Fractals in Rock Mechanics, 2020

From the definition of the capacity dimension, the number of δ-spheres is considered solely, but the number of points covered by each of the δ-spheres could not be analyzed. Thus, a definition of the information dimension is proposed: D1=limδ→0[∑i=1NPilog(Pi)]/logδ; where Pi is the probability for a point of a long time series which falls in the δ-sphere i of the partitioning. The information dimension is a generalization of the capacity dimension. From Equation (2.22), let Pi, = 1/N, then Equation (2.22) becomes Equation (2.20).

Analysis of the blasting effect of strip cartridge position on jointed rock mass

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Journal Information

Published in Mechanics of Advanced Materials and Structures, 2023

Yuantong Zhang, Renshu Yang, Cheng Chen, Chengxiao Li, Haohao Luo

Fractal theory has been widely used to quantitatively describe the complex physical phenomena [21]. The blasting cracks generated in rocks have obvious fractal characteristics, which can be described by fractal dimension [22, 23]. The traditional fractal dimension includes similar dimension, box-counting dimension and information dimension. Since the box-counting dimension method has a simple mathematical expression and can intuitively reflect the occupancy of research object [24–26], this paper uses this method to study the fractal dimension of the surrounding area of the borehole.

Information dimension

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General properties of fractals

Analysis of the blasting effect of strip cartridge position on jointed rock mass