I'm asking how to analyze diagrams like this : http://upload.wikimedia.org/wikipedia/commons/thumb/9/96/Complex_LogGamma.jpg/600px-Complex_LogGamma.jpg
What do distinct colors here mean?
What do the numbers on x,y-axis designate? Are these log-scales?
I think normally the colour represents the phase of the resultant complex number when the function is applied at that point. This wiki page gives a pretty good overview: http://en.wikipedia.org/wiki/Domain_coloring
As for the scale on the axis, they just represent points in the complex plane usually, though for that example it may be log scale, I don't know.