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Brilliant.

Would I be correct in saying that the Mandelbox provides a greater level of varience in detail to the Mandelbulb. I guess the two different objects are only related by the fact that they are both 'escape-time' fractals?

I love it though and cannot get enough of these movies that you guys keep producing!

I think the real reason why the Mandelbox has better variety of shapes is because it is based on conformal mappings ... in other words, it is guaranteed not to have (the equivalent of) whipped cream anywhere at all. The Mandelbulb in contrast is affected by whipped cream almost everywhere, in the sense that the stretchy mappings flatten most of it (especially visible in the ^2 version). We just are not aware of the whipped cream as much, because we direct our attention to the few remaining richer shapes.

In that sense, the Mandelbox is indeed a more faithful analog of the classical 2D Mandelbrot set. Plus, it's full of seemingly straight and circular features, which is rather refreshing for a fractal. Instead of an organic appearance, the Mandelbox has more of a technological or architectural feel.

I applaud thee.  I liked how you changed the colors and how you started by zooming out.