Figure 2
The polynomial f(z) = z2 maps the plane on the left to the plane on the right, the latter being a standard color wheel. The colors of the points on the left plane – the domain – indicate where those points are sent to on the right plane. Colors occur twice on the left image as f doubles the angle; the white region is proportionately larger as f pushes the points away from the unit circle (alas, the figures are not on the same scale). |