Four Dimensional Graphing

Exponential Graphing in Four Dimensions

The standard exponential function given by looks like this:

However, if we allow all complex numbers (for both x and y) instead of only real numbers, we get a four dimensional graph: real x, imaginary x, real y, and imaginary y.

(If that doesn't work, click here for the movie file or click here to see it on YouTube.)
(And if you're running Mac OS X, click here to download the file and experiment with the graph yourself!)