Identify Jumps and Cuts
Branch cuts and jump discontinuities can result in plots that have sharp transitions from one color to another due to not being continuous in a region.
has a branch cut resulting in a sudden jump in the color gradient along the negative real axis. The color spectrum goes around the zero at the origin 1.5 times.
A fractional pole shows a similar jump in the color gradient while proceeding clockwise instead of counterclockwise.
Floor[z] is constant over regions of the complex plane, with sharp jumps from region to region.