An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-11-04 DOI:10.3390/fractalfract7110802

Xuefei Wang

引用次数: 0

Abstract

In this paper, we conduct research on the fractal characteristics of the superposition of fractal surfaces from the view of fractal dimension. We give the upper bound of the lower and upper box dimensions of the graph of the sum of two bivariate continuous functions and calculate the exact values of them under some particular conditions. Further, it has been proven that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of a numerical experiment has been provided to verify our theoretical results. This study can be applied to the fractal analysis of metal fracture surfaces or computer image surfaces.

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分形曲面叠加的分形特性研究

本文从分形维数的角度研究了分形曲面叠加的分形特征。我们给出了两个二元连续函数和图的上下盒维的上界，并计算了它们在某些特定条件下的精确值。进一步证明了两个连续曲面的叠加不能保持分形维数不变，除非它们都是二维的。给出了一个具体的数值实验实例来验证我们的理论结果。本研究可应用于金属断口表面或计算机图像表面的分形分析。

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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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.