量化分形图形的新指数——简便分形指数

A New Index of Quantified Fractal Graphics-Simplified Fractal Index

分形的广泛存在性已被普遍接受，然而分形维数的现有定义计算得到的结果是：不同的分形维数定义得到不同的分形维数值，甚至会出现不同的变化趋势，且在应用时使用的最小二乘回归结果不稳定，导致数值应用也会受影响，出现这些现象主要归咎于现有分形维数定义的严格性、抽象性以及分形图形的码尺效应．为避免这些问题，本文结合分形图形的长尾分布特征及自相似性提出一个新的分形量化形式——简便分形指数，并阐述了该定义背后的分形原理及计算方法，简便分形指数越大，形状复杂程度越高．最后本文利用岩石裂隙图像说明简便分形指数对不同裂隙网络复杂性描述的准确性，验证其作为分形图形量化方法的合理性及便利性．

The existence of the fractal is widely accepted. However, the existing definitions of different fractal dimension result in different fractal dimension values, and even different trends will appear. This is mainly because the results regressed results of the least squares mehtod are not stable, leading to numerical applications will also be affected, these phenomena are mainly attributed to the definition of the existing fractal dimension strictness, abstraction and fractal graphics code effect. In order to avoid these problems, this paper proposes a new fractal quantization form-simplifiued fractal index by combining the long tail distribution and self - similarity of the fractal graph. The fractal principle and calculation method behind the definition are described. The bigger the fractal index is, The higher the shape complexity. In the end, the fractal image is used to illustrate the accuracy of the fractal index to describe the complexity of different fracture networks, and to verify the rationality and convenience of the fractal image quantization method.