There used to be a program for POV-Ray in the 90s called POV-Foam, which made thousands of bubbles to fill a volume, spread over a surface or float in the atmosphere. You could get a long way there simply by filling a cube with foam or blobs. Maybe a couple sets like that, a few booleans, you're just about there.

I never used Pov, but I know there's a Blender addon for it.  I actually came really close by following the tutorial presented earlier in this thread.  The results were surprisingly good, and the mesh was nice and clean.  Thanks very much for the reply!