Abstract. Within the complex dynamics of the solar wind's fluctuating plasma parameters, there is a detectable, hidden order described by a chaotic strange attractor which has a multifractal structure. The multifractal spectrum has been investigated using Voyager (magnetic field) data in the outer heliosphere and using Helios (plasma) data in the inner heliosphere. We have also analyzed the spectrum for the solar wind attractor. The spectrum is found to be consistent with that for the multifractal measure of the self-similar one-scale weighted Cantor set with two parameters describing uniform compression and natural invariant probability measure of the attractor of the system. In order to further quantify the multifractality, we also consider a generalized weighted Cantor set with two different scales describing nonuniform compression. We investigate the resulting multifractal spectrum depending on two scaling parameters and one probability measure parameter, especially for asymmetric scaling. We hope that this generalized model will also be a useful tool for analysis of intermittent turbulence in space plasmas.