2026-06-08T00:02:51Zhttps://docta.ucm.es/rest/oai/request

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 Mera Rivas, María Eugenia Morán Cabré, Manuel 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)) . 2024-01-25T09:27:16Z 2024-01-25T09:27:16Z 2024-01-25T09:27:16Z 2023 journal article 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 http://creativecommons.org/licenses/by-nc-nd/4.0/ restricted access Attribution-NonCommercial-NoDerivatives 4.0 International Springer Nature