Fraction of galaxies containing an X-ray-bright AGN, relative to the background AGN fraction, as a function of projected clustercentric distance r. Magneticum results are shown at low redshift (left panel) and high redshift (bottom right panel) for all galaxies with log M_*(M_⊙) > 10.15 (in red) and only massive galaxies (log M_*(M_⊙) > 11, in blue). The projection depth is 7.6 Mpc. The plot represents the mean profile of many lines of sight and the coloured interval ± standard deviation of different lines of sight. Dotted lines mark the 68% binomial confidence interval when only one line of sight is considered. The confidence intervals of low-mass galaxies are too narrow to be meaningfully displayed. The centralmost bins, influenced by the BCGs, are omitted. The background AGN fraction is defined as the mean fraction in the annulus between 4.5 and 6 R₅₀₀. The fraction at low redshift (left panel) is compared with results of Ehlert et al. (2014) and Koulouridis et al. (2018), from which we also obtained the results of Martini et al. (2007), Koulouridis & Plionis (2010) and Haines et al. (2012). In the upper right panel, we plot the quantity Σ from Fig. 1 in Koulouridis & Bartalucci (2019). The data points from the literature are placed at the centre of radial bins and are shown without the radial errorbars.