Wolfram Mathematica

Different color schemes can be used to highlight features of a complex function.

Define a complex function with a pole at and zeros at , and .

By default, zeros of the complex function are bright and the colors fade to white for large values of relative to the rest of the plot.

Emphasize the zeros by using a globally scaled color function that is black at zeros and white at poles.

Using a locally scaled color function keeps more of the intermediate colors and has better contrast with the black zeros and white poles.

Cyclically darkening the colors based on creates bands and makes it easy to see values that have the same magnitude, even when the function spans a large range of values.

Shade using a color function such that each zero has a small color wheel around it and each pole is surrounded by an accumulation of contours of .

Cyclically darkening the colors using creates bands that make it easy to see values that have the same argument.

Darkening the colors based on both and highlights where the magnitude and arguments are the same.

Darken to give the appearance of curves of constant and and lighten to give the appearance of curves of constant magnitude.