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A new index of quantified fractal graphics – simplified fractal index. (Chinese. English summary) Zbl 1413.28018

Summary: The existence of the fractal is widely accepted. However, the existing definitions of different fractal dimensions result in different fractal dimension values, and even different trends will appear. This is mainly because the regressed results of the least squares method are not stable, leading to that the numerical applications will 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 – simplified 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 is. At 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.

MSC:

28A80 Fractals
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