Colorings
Certainly, we could imagine lots of colorings. The figures below illustrate some.
So instead of the real and imaginary parts we could use only the absolute value of a complex number to define a coloring (like on the top right picture), we could discretize our colorings (as seen on the 2nd and 3rd image of the first row). Furthermore we can define the hue of the assigned color according to the argument—as if winding up a rainbow on a circle centered at the origin—and can make the color darker or lighter according to the magnitude. (This way we would get colorings as seen in the second row. In the case of the 2nd and the 3rd the 'full' colors are to be found on the unit circle.)
Each one of these colorings could come handy in the case of different functions, different situations… And of course many other colorings can be defined.
So thus we know the basic idea of the colorful visualization, let us examine how it works in the case of some specific functions. Jump to the next section: Functions…