I recently began experimenting with fractals when I thought they could
make for appealing and quickly generated layout art in animated content.
I would be really interested in creating 3d fractals. Is there freeware
available for that? What kind of Fractal Software are people using these days?
Greetings, and Welcome to this particular Forum !!!

There are well over 600 fractal rendering applications that are publicly available. At least 40 of these are still actively being developed and are quite popular amongst the fractal enthusiasts. (Most of which are FREE.)
As has already been stated, ChaosPro will produce 3-D type images. And there are several others capable as well. You might try looking through the Software section of this Forum to get you started.