I'm currently doing a couple of 'Ice Cave' renders, and an animation is in the making. I'm not sure if it's going to be any good, because rendering refractive materials is not only extremely slow, but also prone to a lot of unwanted artifacts. But let's put the problems aside for a moment.
I'm going to use the Ice Cave examples to explain something about fractals that I've been thinking about for a while. I'll try to not to get too technical, and anybody with a mild interest in rendering or computer graphics should be able to follow it.
In CG, there's usually a difference between the shape of the object, and its texture. The shape is modeled in some software like digital clay, and then (after the object has been UV unwrapped) the texture is painted on. Now I'm oversimplifying this - in actual fact programs like Z-brush with their abilities to export high-res displacement maps make this distinction a little more fuzzy, but it's still pretty much true.
Take the example of a log of wood. The overall shape is being sculpted, and then a wood texture is applied. In real life though, shape and texture aren't distinct at all. The wood texture consists of little strands of material that make up the whole. To appreciate this connection, consider how the direction of the wood splinters indicate the direction of the tree as a whole.
Unfortunately, I'm not able to model a photo-realistic tree in Mandelbulb3d. But if I was, I wouldn't need to texture it, since the texture would emerge by the sheer fact that in stead of being a solid object, the fractal piece of wood would consist of thousand little wood splinters, giving the appearance of wood. Although usually you only see the outer layer, most fractals are infinitely complex layered objects like onions.
You can see this sub-surface property well in the Ice Cave example. This particular Mandelbulb formula is smooth and round, but it has detail in its surface, as well as holes. This is perfect for the scattering of light in a realistic way inside an object. I'd say I really like the (painterly) texture of this image, but there is no texture. There's only form.
I'm not saying that Mandelbulb3D is the best software for creating realistic ice or sub-surface materials (it isn't), but if this technique would somehow be improved in the future, the processes of modeling and texturing could change completely. In stead of recreating the appearance of a natural object, you would digitally recreate the process that created it. This is already feasible with simple objects like crystal, rock or ice. It would be harder to do for plants and extremely hard to do for animals and humans. But it would unlock an entirely new (semi-photorealistic) realm to render and explore.
I'm sure that some steps have been taken into this direction by clever programmers, and if you know about some cool tool that does this, please let me know in the comments.
VR
I'm considering rendering a VR version of the Ice Caves, although I'd have to think about where the hell I'm going to find enough render power to make that happen. VR is an extremely awesome way to experience fractals, and if you haven't tried it I really recommend trying to get your hand on one of the many VR devices that are coming out this year. There is a great team working on a cross-platform app that you can install on any of the devices (IOS, Android, Oculus, Vive, GearVR) in order to download and watch all my work in the best possible resolution. You should hear more about this when it will release.