Functions of a complex variable in four dimensions

A function of a complex variable represents a 2-manifold embedded in four dimensions. Here, the white grid is the z=x+iy complex plane. The function w=exp(z), or u+iv=exp(x+iy) is projected from four-dimensional (x,y,u,v) space to the screen, in a similar same way a 3D image is projected onto a 2D picture. This projection shows the imaginary part of exp(x+iy). Note that exp(x+iy)=exp(x)*(cos(y)+i*sin(y)). One can seen both the sinousoidal variation with y and the expontial variation with x in this view.