Ehh, Cycles can do some of it. Cycles does support volumetrics, and if you can create a fractal shader, then yes, you can render similar effects. However, note that Cycles doesn’t assign a normal to the ‘border’ of the fractal, so you can’t do very much with the surface shading. The other part where the guy just displaces some geometry with fractals would work fine since Cycles has experimental tesselation and displacement.
Note however that you’d have to construct these fractal shaders yourself and animate their parameters to get any animation.
No idea about c4d and blender versions of octane, you should probably ask on the otoy forums.