In this chain starting from the red initial seed, after a few steps grazing a critical curve, the e from Eq. (18), represented here in orange, is too long and worsens the fulfillment of the lens equation. At this point, the κ-correction (32), represented by the green step, pushes the chain closer to the critical curve, where the lens equation is closer to being fulfilled. This correction is important in order to accurately follow the vector flow all around the critical curves.