EXAMPLES OF USING BINARY CANTOR SETS TO STUDY THE CONNECTIVITY OF SIERPINSKI RELATIVES

被引：8

作者：

Taylor, T. D. ^{[1
]}

Hudson, C. ^{[1
]}

Anderson, A. ^{[1
]}

机构：

[1] St Francis Xavier Univ, Dept Math Stat & Comp Sci, Antigonish, NS B2G 2W5, Canada

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2012年 / 20卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Sierpinski Relatives; Iterated Function Systems; Connectivity; Cantor Sets; LACUNARITY;

D O I：

10.1142/S0218348X12500065

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Sierpinski relatives form a class of fractals that all have the same fractal dimension, but different topologies. This class includes the well-known Sierpinski gasket. Some relatives are totally disconnected, some are disconnected but with paths, some are simply-connected, and some are multiply-connected. This paper presents examples of relatives for which binary Cantor sets are relevant for the connectivity. These Cantor sets are variations of the usual middle thirds Cantor set, and their binary descriptions greatly aid in the determination of the connectivity of the corresponding relatives.

引用

页码：61 / 75

页数：15

共 13 条

[1] CHARACTERIZING THE LACUNARITY OF RANDOM AND DETERMINISTIC FRACTAL SETS [J].

ALLAIN, C ;

CLOITRE, M .

PHYSICAL REVIEW A, 1991, 44 (06) :3552-3558

[2]

Frantz M, 2004, P SYMP PURE MATH, V72, P77

[3] Lacunarity of self-similar and stochastically self-similar sets [J].

Gatzouras, D .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (05) :1953-1983

[4] Barcodes: The persistent topology of data [J].

Ghrist, Robert .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 45 (01) :61-75

[5] WHATS THE DIFFERENCE BETWEEN CANTOR SETS [J].

KRAFT, RL .

AMERICAN MATHEMATICAL MONTHLY, 1994, 101 (07) :640-650

[6]

Mandelbrot B., 1982, FRACTAL GEOMETRY NAT

[7] ANTIPODAL CORRELATIONS AND THE TEXTURE (FRACTAL LACUNARITY) IN CRITICAL PERCOLATION CLUSTERS [J].

MANDELBROT, BB ;

STAUFFER, D .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1994, 27 (09) :L237-L242

[8]

Peitgen HO., 1992, Chaos and fractals, V7

[9] CONNECTIVITY PROPERTIES OF SIERPINSKI RELATIVES [J].

Taylor, T. D. .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2011, 19 (04) :481-506

[10] A NEW CLASSIFICATION OF NON-OVERLAPPING SYMMETRIC BINARY FRACTAL TREES USING EPSILON HULLS [J].

Taylor, T. D. .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2009, 17 (03) :365-384

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