Spherical slices through the ensemble mean of the three-dimensional initial (left panel) and final density field (right panel) and corresponding pixel-wise variances (lower panels) at a distance of R = 100 h⁻¹ Mpc from the observer. It is interesting to note, that the pixel-wise variance for the final density field imprints the cosmic large scale structure. Correlations between signal and noise are expected for any point process, such as the generation of galaxy observations. The BORG algorithm correctly accounts for these effects.