On the packing measure of the Sierpinski gasket



Downloads per month over past year

LLorente Comí, Marta and Mera Rivas, Maria Eugenia and Morán Cabré, Manuel (2018) On the packing measure of the Sierpinski gasket. Nonlinearity, 31 (6). pp. 2571-2589. ISSN 0951-7715

[thumbnail of version final(previa prueba imprenta).pdf]

Official URL: https://doi.org/10.1088/1361-6544/aab31c


We show that the s-dimensional packing measure P^{s}(S) of the Sierpinski gasket S, where s=((log3)/(log2)) is the similarity dimension of S, satisfies 1.6677≤P^{s}(S)≤1.6713.
We present a formula (see Theorem 6) that enables the achievement of the above measure bounds for this non-totally disconnected set as it shows that the symmetries of the Sierpinski gasket can be exploited to simplify the density characterization of P^{s} obtained in Morán M. (Nonlinearity, 2005) for self-similar sets satisfying the so-called Open Set Condition. Thanks to the reduction obtained in Theorem 6 we are able to handle the problem of computability of P^{s}(S) with a suitable algorithm.

Item Type:Article
Uncontrolled Keywords:Sierpinski gasket; Packing measure; Computability of fractal measures; Algorithm; Self-similar sets.
Subjects:Sciences > Mathematics
ID Code:58898
Deposited On:17 Feb 2020 12:52
Last Modified:17 Feb 2020 12:52

Origin of downloads

Repository Staff Only: item control page