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Ok I've given it a go. The 2D mandelbox is not as amazing as it's 3D counterpart, nor as interesting as the Mandelbrot set itself. I've played around with a hybrid of the two and found some interesting results.


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4360


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4359

I remember seeing that image but I had assumed it was looking flat on at a 3D Mandelbox - it does appear to have 3 dimensionality - and a light source... And it does look like it has more in common with the 3D Mandelbox than (at least my efforts at) 2D Mandelboxes. For instance in Mandelbulber (with which I only have a passing familiarity with) until you hit 'render 3d' you get a 2d version - but as a slice through a 3d fractal.

The images I posted above are purely 2D fractals - no slicing! The formula I'm using here (in a pseudo-pseudo code):

http://www.fractalforums.com/programming/understanding-the-mandelbox-formula-(for-2d)

Here's another hybrid almost as if to prove that the 2D mandelbox/mandelbrot hybrid is more mandelbox-like than the pure mandelbox. But then maybe I've got something wrong somewhere  : 

A quick vid I did in order for my laptop at work not to stay too idle while I'm on the phone or in meetings
This is actually a cut of a 3D box.

<a href="http://www.youtube.com/v/Vo0AbqJGFUY&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Vo0AbqJGFUY&rel=1&fs=1&hd=1</a>

And this one is a real 2D image made with Mandelbulb3D, which could also be called Mandelbulb2D


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4386