Map of overdensity. The purple regions are below the selected overdensity threshold. The map also contains the computed constant radius, dashed blue line, and the variable radius R(l), indicated with a solid blue line. In the right panel, at each r, we have plotted the frequencies of overdense cells (red line for cells above that r and green line for cells below r) and their difference (yellow line). The constant radius is shown as the radius where the difference in overdense cells is maximum. The variable radius R(l) is plotted at the bottom of the figure. The grey solid line is the calculated radius, while the black dashed line is the radius with the applied Gaussian filter. The dark and red clumps at larger r correspond to a larger overdensity of particles related to substructures. We obtained this map for one of the filaments in the D6 region (AGN simulation).