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oai:docta.ucm.es:20.500.14352/952942025-08-28T14:46:27Zcom_20.500.14352_14col_20.500.14352_15

Irregularity Index and Spherical Densities of the Penta-Sierpinski Gasket Indice de irregularidad y densidades esféricas de la penta alfombra de Sierpinski Mera Rivas, María Eugenia Morán Cabré, Manuel 5 Self-similar sets Penta-Sierpinski gasket Packing measure Centred Hausdorff measure Density of measures Asymptotic spectrum Computability in fractal geometry Ciencias Matemáticas (Matemáticas) Geometría 12 Matemáticas 1202 Análisis y Análisis Funcional 1204 Geometría 1206 Análisis Numérico We compute the centred Hausdorff measure, Cs(P) ∼ 2.44, and the packing measure, Ps(P) ∼ 6.77, of the penta-Sierpinski gasket, P, with explicit error bounds. We also compute the full spectra of asymptotic spherical densities of these measures in P, which, in contrast with that of the Sierpinski gasket, consists of a unique interval. These results allow us to compute the irregularity index of P, I(P) ∼ 0.6398, which we define for any self-similar set E with open set condition as I(E) = 1 − (Cs(E)/Ps(E)) . Universidad Complutense de Madrid Banco Santander Depto. de Análisis Económico y Economía Cuantitativa Fac. de Ciencias Económicas y Empresariales Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2024-01-25T09:27:16Z 2024-01-25T09:27:16Z 2023 journal article VoR https://hdl.handle.net/20.500.14352/95294 1660-5446 10.1007/s00009-023-02528-6 1660-5454 eng (PR108/20-14) Mera, M.E., Morán, M. Irregularity Index and Spherical Densities of the Penta-Sierpinski Gasket. Mediterr. J. Math. 20, 322 (2023). https://doi.org/10.1007/s00009-023-02528-6 Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ restricted access application/pdf Springer Nature