On the packing measure of the Sierpinski gasket

Abstract

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.