Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices

被引：37

作者：

Falconer, Kenneth ^{[1
]}

Miao, Jun ^{[1
]}

机构：

[1] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2007年 / 15卷 / 03期

关键词：

fractals; multifractals; self-affine;

D O I：

10.1142/S0218348X07003587

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider calculation of the dimensions of self-affine fractals and multifractals that are the attractors of iterated function systems specified in terms of upper-triangular matrices. Using methods from linear algebra, we obtain explicit formulae for the dimensions that are valid in many

引用

页码：289 / 299

页数：11

共 13 条

[1]

[Anonymous], 2003, FRACTAL GEOMETRY, DOI DOI 10.1002/0470013850

[2]

Barros M.P., 1995, BIOCIENCIAS, V3, P239

[3]

EDALAT A, 1998, ELECT NOTES THEOR CO, V13

[4] Generalized dimensions of measures on self-affine sets [J].

Falconer, KJ .

NONLINEARITY, 1999, 12 (04) :877-891

[5] Fractal properties of generalized Sierpinski triangles [J].

Falconer, KJ ;

Lammering, B .

FRACTALS-AN INTERDISCIPLINARY JOURNAL ON THE COMPLEX GEOMETRY OF NATURE, 1998, 6 (01) :31-41

[6]

HEUTER I, 1995, ERGOD THEOR DYN, V15, P77

[7] HAUSDORFF AND BOX DIMENSIONS OF CERTAIN SELF AFFINE FRACTALS [J].

LALLEY, SP ;

GATZOURAS, D .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1992, 41 (02) :533-568

[8]

Lancaster P., 1969, THEORY MATRICES

[9] THE HAUSDORFF DIMENSION OF GENERAL SIERPINSKI CARPETS [J].

MCMULLEN, C .

NAGOYA MATHEMATICAL JOURNAL, 1984, 96 (DEC) :1-9

[10]

Northcott D. G., 1984, MULTILINEAR ALGEBRA

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