Earlier this year, I started working through the online book Ray Tracing In One Weekend (Book 1). I have been following along with it in Common Lisp, and I have been extending it all from 3-dimensional to n-dimensional.
I reproduced 4-dimensional versions of all of the book images which you can see on my weekend-raytracer github page.
Here is the final image. This is a 250-samples-per-pixel, 640x360x10 image plane of three large hyperspheres (one mirrored, one diffuse, one glass) atop a very large, diffuse hypersphere. Also atop this very large hypersphere are a bunch of smaller hyperspheres of varying colors and materials. The image is rendered with some defocus-blur.
Caveat: This depends on a patched version of the policy-cond library that is not in the current Quicklisp distribution but should be in the next.