### 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` = e^{z}, or
`u` + `iv` = e^{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 e^{x + iy} = e^{x}(cos `y` + i sin `y`). One can see both the sinusoidal variation with y and the exponential variation with x in this view.