Radial profile of the fraction of binaries in P1 (blue), P2 (red), and both populations (black) evolved to 4 Gyr (top), 8 Gyr (middle), and 12 Gyr (bottom) for simulation mr025c005fb10. We report the median of 100 random realizations of the 2D spatial projection, with the shaded regions representing the 25th and 75th percentiles. The horizontal dashed lines represent the global value of the binary fraction for P1 (blue dashed line), P2 (red dashed line), and P1+P2 (black dashed line). Binary fraction refers to the fraction of objects within the total system that are binaries (see Eq. (4)).