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The varying shapes of this fractal reminded me a machine to crush something, so I just called it Mandelbox (litteraly Almond box) even though it's just a kaleidoscopic IFS
http://www.youtube.com/watch?v=a_1abC02gYg

And this one is just a quick exploration and zoom (no transformations) of another K-IFS fractal. I called it moon rising because....just search for "moon rising" in youtube and you will understand !
http://www.youtube.com/watch?v=tOAxheyZiVI

Just like 20 years when I longed for the days I could zoom around the (2D) mandelbrot in realtime - I now long for the days when I can zoom around these amazing 3D fractals in realtime! In another 20 years perhaps?

Somewhat less than 20 years

See http://www.fractalforums.com/3d-fractal-generation/where-are-the-realtime-gpu-mandelboxeds/msg18954/#msg18954 for a start - and with a little digging you'll find some GPU renderers for the Mandelbulb too - so far no hybrids on the GPU though ?

It  is HUGE bib! 
Glad you zoomed in on anouther part than the zoom out!

Irrespective of the software there are basically two main types of "shimmering" bits.
The first is simple aliasing usually due to trying to render a fractal to a higher resolution than the actual pixel size which can be fixed (or at least improved) by keeping the same render size and reducing the mathematical resolution or by keeping the same mathematical resolution and increasing the render size. (In most 3D fractals the mathematical resolution is controlled using a combination of distance estimation solid threshold and/or bailout value and/or maximum iteration count).
The second is more troublesome in terms of removal because to improve it generally means increasing the accuracy of calculation (e.g. reducing the step sizes in ray-tracing) because the problem is usually inaccuracies in calculating surface collisions - always more noticeable on thinner parts of a fractal which tend to appear and disappear in an animation when the problem occurs. Of course reducing the step sizes has a considerable speed penalty when rendering.