THE CENTERED HAUSDORFF MEASURE OF THE SIERPIŃSKI GASKET

Marta Llorente (), Marã A Eugenia Mera () and Manuel Morã N
Additional contact information
Marta Llorente: Departamento de Análisis Económico
Marã A Eugenia Mera: ��Departamento de Análisis Económico y Economía Cuantitativa, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Madrid, Spain
Manuel Morã N: ��Departamento de Análisis Económico y Economía Cuantitativa, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Madrid, Spain‡Institute of Interdisciplinary Mathematics (IMI), Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-15

Abstract: We show that the centered Hausdorff measure, Cs(S), with s = log 3 log 2, of the Sierpiński 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 Cs(S) is A-computable (algorithmic-computable) in the sense that there is an algorithm that converges to Cs(S), with explicit error bounds. Using this algorithm we show that Cs(S) ∼ 1.0049.

Keywords: Self-similar Sets; Sierpiński Gasket; Hausdorff Measures; Density of Measures; Computability of Fractal Measures (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X23501074
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:31:y:2023:i:09:n:s0218348x23501074

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X23501074

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().