THE CENTERED HAUSDORFF MEASURE OF THE SIERPINSKI GASKET

被引：1

作者：

Llorente, Marta ^{[1
]}

Mera, Maria Eugenia ^{[2
]}

Moran, Manuel ^{[2
,3
]}

机构：

[1] Univ Autonoma Madrid, Dept Anal Econ Econ Cuantitat, Campus Cantoblanco, Madrid 28049, Spain

[2] Univ Complutense Madrid, Dept Anal Econ & Econ Cuantitat, Campus Somosaguas, Madrid 28223, Spain

[3] Univ Complutense Madrid, Inst Interdisciplinary Math IMI, Plaza Ciencias 3, Madrid 28040, Spain

来源：

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

关键词：

Self-similar Sets; Sierpiski Gasket; Hausdorff Measures; Density of Measures; Computability of Fractal Measures; SELF-SIMILAR SETS; PACKING MEASURE; COMPUTABILITY;

D O I：

10.1142/S0218348X23501074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the centered Hausdorff measure, C-s(S), with s = log 3/log 2, of the Sierpinski gasket S, is C-computable (continuous-computable), in the sense that its value is the solution of the minimization problem of a continuous function on a compact domain. We also show that C-s(S) is A-computable (algorithmic-computable) in the sense that there is an algorithm that converges to C-s(S), with explicit error bounds. Using this algorithm we show that C-s(S) similar to 1.0049.

引用

页数：15

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