Constant
A constant function assigns the same complex number to each and every complex number. So we should paint each point (pixel) the same color.
\(f(z) = 0,\quad z \in \mathbb{C}(0,3)\)
Thus we might be not so surprised to get a big monochrome square. In the case of this coloring and the value zero it is 'Deep Purple'.
Obviously now it is irrelevant which domain we have chosen.