具有分形维数的正则分形函数的局部结构

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-10-12 DOI:10.1142/s0218348x23501189

Q. Zhang, L. J. Lu

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引用次数: 0

摘要

本文探讨了具有一定分形维数的分形函数的局部结构和分形特征。证明了与相应分形函数上盒维数振荡幅值不一致的点是无密点的结论。这将对探索分形函数组合的分形维数估计起到重要的支撑作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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REMARKS ON THE LOCAL STRUCTURE OF REGULAR FRACTAL FUNCTIONS WITH FRACTAL DIMENSIONS

In this paper, we have explored the local structure and fractal characteristics of fractal functions with certain fractal dimensions. The conclusion that points with inconsistent oscillation amplitudes with the upper Box dimension of the corresponding fractal functions have been proved to be nowhere dense. This will play an important supporting role in exploring the fractal dimension estimation of the combination of fractal functions.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.