BOX DIMENSIONS OF α-FRACTAL FUNCTIONS

被引：36

作者：

Akhtar, Md. Nasim ^{[1
]}

Prasad, M. Guru Prem ^{[1
]}

Navascues, M. A. ^{[2
]}

机构：

[1] Indian Inst Technol Guwahati, Dept Math, Gauhati 781039, Assam, India

[2] Univ Zaragoza, Dept Mate Aplicada, E-50009 Zaragoza, Spain

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2016年 / 24卷 / 03期

关键词：

Fractal Interpolation Functions; alpha-Fractal Interpolation Functions; Variation of Continuous Functions; Box-Counting Dimensions; INTERPOLATION SURFACES;

D O I：

10.1142/S0218348X16500377

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The box dimension of the graph of non-affine, continuous, nowhere differentiable function fa which is a fractal analogue of a continuous function f corresponding to a certain iterated function system (IFS), is investigated in the present paper. The estimates for box dimension of the graph of alpha-fractal function f(alpha) for equally spaced as well as arbitrary data sets are found.

引用

页数：13

共 50 条

[1] On the Lower and Upper Box Dimensions of the Sum of Two Fractal Functions
Yu, Binyan
Liang, Yongshun
[J]. FRACTAL AND FRACTIONAL, 2022, 6 (07)
[2] FRACTAL DIMENSIONS OF LINEAR COMBINATION OF CONTINUOUS FUNCTIONS WITH THE SAME BOX DIMENSION
Wang, Xuefei
Zhao, Chunxia
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (07)
[3] Box-counting dimensions of fractal interpolation surfaces derived from fractal interpolation functions
Feng, Zhigang
Sun, Xiuqing
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 412 (01) : 416 - 425
[4] ON FRACTAL DIMENSIONS OF FRACTAL FUNCTIONS USING FUNCTION SPACES
Chandra, Subhash
Bbas, Syed A.
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 106 (03) : 470 - 480
[5] Box dimension for graphs of fractal functions
Brown, G
Yin, QH
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1997, 40 : 331 - 344
[6] Graphs of continuous functions and fractal dimensions
Verma, Manuj
Priyadarshi, Amit
[J]. CHAOS SOLITONS & FRACTALS, 2023, 172
[7] FRACTAL DIMENSIONS OF THE LOGARITHM OF CONTINUOUS FUNCTIONS
Liu, Peizhi
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (01)
[8] A FAST ALGORITHM TO DETERMINE FRACTAL DIMENSIONS BY BOX COUNTING
LIEBOVITCH, LS
TOTH, T
[J]. PHYSICS LETTERS A, 1989, 141 (8-9) : 386 - 390
[9] Box-counting dimensions of generalised fractal nests
Milicic, Sinisa
[J]. CHAOS SOLITONS & FRACTALS, 2018, 113 : 125 - 134
[10] AN OPTIMIZED BOX-ASSISTED ALGORITHM FOR FRACTAL DIMENSIONS
GRASSBERGER, P
[J]. PHYSICS LETTERS A, 1990, 148 (1-2) : 63 - 68

← 1 2 3 4 5 →