The Complex Cubing Function (Polar Coordinates)

Consider the graph of the cubing function, w = z3, where the domain is restricted to the unit disc. The view on the left below reprents the real-part of the graph of this function, and on the right, the imaginary part. The movie shows the rotation that moves between the two.


Notice that the red and green axes remain the same (these are the x and y axes) while the third axis goes from blue to white, indicating the change from seeing the u axis to seeing the v axis. In the movie, the surface seems simply to rotate in three-space, but notice that the coloration does not shift with the surface, so this is not a rotation in three-space, but different views of the object in four-space.