  Anderson localization does not lead to an exponential decay of intensity of
an incident wave with the depth inside a strongly disordered three-dimensional
medium. Instead, the average intensity is roughly constant in the first half of
a disordered slab, sharply drops in a narrow region in the middle of the
sample, and then remains low in the second half of the sample. A universal,
scale-free spatial distribution of average intensity is found at mobility edges
where the intensity exhibits strong sample-to-sample fluctuations. Our
numerical simulations allow us to discriminate between two competing local
diffusion theories of Anderson localization and to pinpoint a deficiency of the
self-consistent theory.
