Including emission along a path (Schwarzchild's equation), a flux will
approach saturation as the optical thickness
becomes large over scales where the temperature variation is small; at smaller optical thicknesses, the temperature distribution may
vary and larger temperature variations make the nonlinearity of the Planck function important, but over short distances, the temperature variation can be approximated as linear and the associated Planck function values can be approximated as linearly proportional to distance for small temperature changes, so the flux will
approach an asymptotic value as a hyperbolic function (the difference between the flux and the saturation value of the flux will be proportional to 1 / optical thickness per unit distance (assuming isotropic optical properties (or even somewhat anisotropic properties), it will have that proportionality for all directions and thus for the whole flux across an area).
Blogs are obviously
varied in the formality with which they cover and
approach a field of interest and some could perhaps begin to approximate the level of publishing in recognized journals, but then they would
become that venue and lose some of the positive characteristics that are associated with what currently is more typical of blogs (at least good ones).