Visualizing multi-valued complex functions w = √z and w = log(z). The domain coloring shows arg(w) as hue and |w| as brightness, revealing the branch cut and monodromy.
Domain coloring: hue encodes argument of w, brightness encodes |w|. The branch cut runs along the negative real axis. Going around the branch point (origin) once changes the sheet — this is monodromy. log(z) has infinitely many sheets (n·2πi shifts).