I feel fortunate to work on a field where not only I deal on a daily basis with plenty of algorithms worth visualizing, but my job itself is to develop algorithms -to- visualize. This is, the end goal of the algorithms I work with is to visualize (photo-real) stuff.
For example, here’s a visualization of the highly efficient fiber-field rendering routines (hair/fur) that I’ve been working on during the past months. This image was rendered by Erwann Loison in Arion 3. But, if you want to put it this way, an Arion render is nothing but a visualization of the light simulation algorithms that are running inside.
Now, here’s a much more spartan visualization of some of the routines involved in Arion’s hair/fur rendering. This is an image taken from the RCSDK Unit Testing system. It visualizes some of my custom ray-to-primitive intersection routines (e.g., infinite planes, spheres, cylinders, cones, and connectable fiber (hair) segments).