This app makes it super fun to examine 3D fractals. I've been interested in Tom Beddard's work for a few years, ever since seeing his 3D fractals on Vimeo.
Cool. I have implemented some of these myself (menger sponge, mandelbox, mandelbulb) in a real time form in Unreal a while back. I think i posted them in my unreal thread. They did not have fancy lighting in the most of them though. I used distance functions in my implementations but classic ray-box/sphere intersections works just as well. Distance functions allows for easy displacement and domain warping though.
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https://www.shadertoy.com/ has a whole bunch of these and its also a good reference for implementing them. just type the name of the fractal into the search bar and itll likely give you a few. This wiki page also has a picture of a lot of them:https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension