Full matrix of the correlation strength between different parameters, with darker colors indicating stronger correlations, for all four simulations as indicated at the respective tiles for each panel. From top to bottom and left to right are the same parameters, in the following order: formation redshift z_form, the fraction of stellar mass within ICL plus BCG f_{ICL + BCG}, the center shift between the stellar (s_stars) or gas barycenter (s_gas) and the BCG, the fraction of total mass within all substructures f_sub or within just the 8th most massive substructure f₈, the stellar mass ratio between the BCG and the second (M12) or fourth (M14) most massive galaxy in a cluster, the central stellar potential ϕ_BCG, the passive fraction f_quench of galaxies in the cluster with stellar masses above 1 × 10¹⁰ M_⊙ as well as their total number N_sat, and the total halo mass M_200c. We note that black squares in the diagonal mark the self-correlation of the parameters and are thus all equal to one.