These are beautiful. What sort of prerequisite knowledge is needed to make some of this stuff happen? I already know some OpenGL but I doubt I've got the math training to understand the formulas here.
My math training is virtually nonexistent when it comes down to this, I took a course that's a lower level than Linear Algebra 101, and can't code my way out of a paper bag. I do try and understand some of the formulas behind some of the stuff I made, but more times than not I just give up and fiddle with variables either in an attempt to understand, or just to see what happens. If you want to be one of the people who write the formulas I bash together like action figures, then you might need some real linear algebra to understand how to map transformations of functions in 4 dimensional space to 3 dimensional space or whatever some of these formulas actually calculate
The program I use is Mandelbulb 3D
and it's fairly easy to use and there are tutorials available, you might need a GPU to render these, but if you can play PC games of any sort on your PC then you're probably fine.