I think a fractal is defined as a shape that is self similar
which means you can cut out a little bit of it, and zoom it up and you get a copy of the original. The Mandelbox uses a similar set of equations to the Mandelbrot set, just over 3-D space with a couple of transformations to make it more "boxy" and 3-D.
Fractals are a bit weird. Take that triangle one, (Sierpinski Gasket) for example. If you stick three copies of it together, in a triangle, you get a Sierpinski Gasket twice as big as what you started with. Fair enough, you might think, but think about this - if you wanted to make a simple 2-D triangle twice as big, you'd have to put four copies of it together. And if you wanted to make a line drawing of a triangle twice as big, you could make it out of the lines from two copies. So the Sierpinski Gasket isn't really a 1-D drawing or a 2-D drawing. I think it's technically a 1.585-D drawing, more or less.
(, Tue 29 Jun 2010, 14:03, Reply)