  Complexity theory embodies some of the hardest, most fundamental and most
challenging open problems in modern science. The very term complexity is very
elusive, so that the main goal of this theory is to find meaningful quantifiers
for it. In fact we need various measures to take into account the multiple
facets of this term. Here some biparametric Cr\'amer-Rao and Heisenberg-R\'enyi
measures of complexity of continuous probability distributions are defined and
discussed. Then, they are applied to the blackbody radiation at temperature T
in a d-dimensional universe. It is found that these dimensionless quantities do
not depend on T nor on any physical constants. So, they have an universal
character in the sense that they only depend on the spatial dimensionality. To
determine these complexity quantifiers we have calculated their dispersion
(typical deviations) and entropy (R\'enyi entropies and the generalized Fisher
information) constituents. They are found to have a temperature-dependent
behavior similar to the celebrated Wien's displacement law of the dominant
frequency $\nu_{max}$ at which the spectrum reaches its maximum. Moreover, they
allow us to gain insights into new aspects of the d-dimensional blackbody
spectrum and about the quantification of quantum effects associated with space
dimensionality.
