Visualization of Complex Functions: the Exponential Y = e ^ X

For Y = y1 + i y2 and X = x1 + i x2, the function Y = Y(X) is a 4D surface in space (X,Y) ~ (x1, x2, y1, y2). Let us project this "simply" unto our 2D screen ...

[DMovie]

Koji Miyazaki of Kyoto University would appreciate your work. As a matter of fact, so would have Arthur Loeb and his friend H. S. M. Coxeter.