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The Centered Hausdorff Measure Of The Sierpiåƒski Gasket

Author

Listed:
  • 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)

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.

Suggested Citation

  • Marta Llorente & Marã A Eugenia Mera & Manuel Morã N, 2023. "The Centered Hausdorff Measure Of The Sierpiåƒski Gasket," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-15.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:09:n:s0218348x23501074
    DOI: 10.1142/S0218348X23501074
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