Just recently, in fact a new method came along: those raymarchers that many modern 4k intros are, are essentially a single pixel shader. The C code draws a single quad that fills the screen two-dimensionally, and calls the shader. The shader computes a colour for each pixel for each frame, on the GPU, using relatively simple math to describe the scene (geometric shapes, like intersections of spheres and cubes, for instance. or fractals, like in the OP).
This means that instead of learning sizecoding, the opengl/d3d pipeline, mesh uploading, textures, getting along with the video bus speed, index buffers, geometry shaders, and so on, and so on, you can just learn GLSL and how a raymarcher works. Much like 20 years ago, getting something on screen quickly became easy again. It's not as easy as Processing, but it's not too far off either.
For example, check out this video[1] about the Russian demogroup Quite (who made the amazing 4k intro "cdak"[2]. The video briefly shows (scroll to 20 minutes) how unc starts with the shader instead of with the C code, using vvvv[3], a tool for live prototyping realtime graphics. They only turn the non-shader parts of the vvvv "code" (block diagrams and envelopes) into C code when the intro starts looking like it's going to be releaseable. With such an approach, you get motivated real fast; focus on getting something on screen, worry about getting into a demoparty compo later.
Or just don't worry about the C version at all, and make something cool that you'll never be able to pull off with any animation studio, and put it on vimeo :-)
Oh, also check out this Pouet thread [4] about how Quite made "cdak" (but first see the intro!). It's one of those things that make you even more amazed when you get it.
[1] http://www.youtube.com/watch?v=tuoRpEMfEHY
[2] http://www.pouet.net/prod.php?which=55758 | http://www.youtube.com/watch?v=RCh3Q08HMfs
[3] http://vvvv.org/
[4] http://www.pouet.net/topic.php?which=7909&page=1&x=2...