I published my attempts at 3D fractals here in the resources section before, that includes Mandelbox.
I used a different approach though, the actual 3D shape is created out of test voxels and an Instanced Mesh is used to speed things up. It’s harder to make a nice visual because you need to remove some of the voxels based on escape condition.
Here is a decent Mandelbox attempt: choose max box -2.25 from the presets menu and press generate.
I believe Mandelbulb can be done the same way, by applying a different formula.
This approach is pretty computationally restrictive though, to reduce the number of elements, an extra algorithm needs to be put into place to exclude voxels in the middle of bulk pieces, so you only generate a surface. I’m still thinking about how to do it the best way.
Here is a JS module with classes to make different 3D fractals.