What we have here is a little gem called Mandelbulb 3D (MB3D) that I discovered recently when I was googling around for what kind of fractal generator programs are out there. It's a freeware program that you can download here:
Unzip that to wherever and you'll run the .exe right from the folder, no installation necessary.
So the kicker with this thing is, when you load in a fractal formula and hit the "Calculate 3d" button, you can explore your fractal in 3D space! It turns the fractal into an entire world you can zoom and pan around in, find new cracks or holes, zoom into those and find more worlds inside of those. The pics below are 2D and 3D versions of the same fractal.
Out of the box it comes with plenty of incredible fractal formulas to play with, and you can add up to 6 formulas together to get some crazy results. Even within one formula there's usually so many parameters to play with that you'll end up with something far removed from the original very quickly. And once you find a spot in your fractal that looks good you can add ambient light, volumetric lighting, hard and ambient shadows, depth of field, reflections, textures, background images, and colors before rendering out to an image resolution of your choosing. Here's one that I created after following a tutorial and just tweaking around for about 15 minutes
And here's the kind of stuff experienced users are creating with MB3D (and I'm sure combined with Photoshop for some post-processing in many cases). These are a couple pieces by one of my favorite fractal artists batjorge
(Dark Matter by batjorge)
(Sweet Notions of Decay by batjorge)
Getting started is really easy, but understanding what all the values do will take some time to learn. Sometimes you can hose your fractal completely by just altering a parameter by 0.01, and other times changing the values will make no noticeable change at all, you'll just have to play around. The good thing is there's a great community for this, and you can find a wealth of tutorials and resources at fractalforums if you find yourself really getting into this. There's a great sharing feature of the program too, where you can paste in simple text parameters that someone's shared and view and build upon others' creations. Make something cool? Just paste your parameters to someone and they can check it out themselves.
But for just getting started I would check out these tutorials, which I was able to get through without too many problems:
Well, there's the quick and dirty on MB3D! Hope you enjoy! Hey if you make something neat go ahead and paste your params in the comments :)