Probability distribution of column densities faced by 910 Å photons. The three filled histograms correspond to the three directions that have the same color in Sect. 3. The cyan dashed line is the average distribution over the 1728 directions of the three outputs. It has a covering fraction of 93%. Molecular hydrogen chemistry is not considered in the simulation, and so the real atomic hydrogen column densities should saturate around 10²³ cm⁻².