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

被引：1

作者：

Zhang, Q. ^{[1
]}

Lu, L. J. ^{[2
,3
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 211106, Peoples R China

[2] Nanjing Univ, Business Sch, Nanjing 210008, Peoples R China

[3] Wuxi TaiHu Univ, Wuxi 214063, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2023年 / 31卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Fractal Dimensions; Regular Fractal Functions; Variation; Fractal Characteristic; Local Structure;

D O I：

10.1142/S0218348X23501189

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：5

共 11 条

[1] ON FRACTAL DIMENSIONS OF FRACTAL FUNCTIONS USING FUNCTION SPACES [J].

Chandra, Subhash ;

Bbas, Syed A. .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 106 (03) :470-480

[2] Analysis of fractal dimension of mixed Riemann-Liouville integral [J].

Chandra, Subhash ;

Abbas, Syed .

NUMERICAL ALGORITHMS, 2022, 91 (03) :1021-1046

[3]

Falconer K., 2004, Fractal Geometry: Mathematical Foundations and Applications

[4] PROGRESS ON ESTIMATION OF FRACTAL DIMENSIONS OF FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS [J].

Liang, Yong-Shun .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2019, 27 (05)

[5]

[梁永顺 Liang Yongshun], 2016, [中国科学. 数学, Scientia Sinica Mathematica], V46, P423

[6]

Mandelbrot B., 1982, FRACTAL GEOMETRY NAT

[7] Graphs of continuous functions and fractal dimensions [J].

Verma, Manuj ;

Priyadarshi, Amit .

CHAOS SOLITONS & FRACTALS, 2023, 172

[8] Dimensions of new fractal functions and associated measures [J].

Verma, Manuj ;

Priyadarshi, Amit .

NUMERICAL ALGORITHMS, 2023, 94 (02) :817-846

[9] Dimension preserving approximation [J].

Verma, S. ;

Massopust, P. R. .

AEQUATIONES MATHEMATICAE, 2022, 96 (06) :1233-1247

[10]

Wen Z.Y, 2000, Mathematical Foundations of Fractal Geometry

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