Inspired by a great video on the Laplace transform, I was looking for an easy way to visualize complex functions of time, i.e., functions of time where the output is a complex number. This is fairly easy to do with Guile Scheme and Gnuplot, though the method could be polished more into a proper application, which I didn’t do.

We just pass in the starting value (t0), the maximum time value, a step value (usually some fraction of Pi), and a lambda with our complex function of time. Writing complex functions of time is pretty easy in Guile Scheme because all the numbers are represented internally as complex numbers anyway. E.g.: