How would you continuously improve the mandelbrot fractal?

I've seen many mandelbrot image generator drawing a low resolution fractal of the mandelbrot and then continuously improve the fractal. Is this a tiling algorithm? Here is an example: http://neave.com/fractal/

Update: I've found this about recursively subdivide and calculate the mandelbrot: http://www.metabit.org/~rfigura/figura-fractal/math.html. Maybe it's possible to use a kd-tree to subdivide the image?

Update 2: http://randomascii.wordpress.com/2011/08/13/faster-fractals-through-algebra/ Update 3: http://www.fractalforums.com/programming/mandelbrot-exterior-optimization/15/

I think that site is not as clever as you give it credit for. I think what happens on a zoom is this:

• Take the previous image, scale it up using a standard interpolation method. This gives you the 'blurry' zoomed in image. Click the zoom in button several times to see this best
• Then, in concentric circles starting from the central point, recalculate squares of the image in full resolution for the new zoom level. This 'sharpens' the image progressively from the centre outwards. Because you're probably looking at the centre, you see the improvement straight away.

You can more clearly see what it's doing by zooming far in, then dragging the image in a diagonal direction, so that almost all the screen is undrawn. When you release the drag, you will see the image rendered progressively in squares, in concentric circles from the new centre.

I haven't checked, but I don't think it's doing anything clever to treat in-set points differently - it's just that because an entirely-in-set square will be black both before and after rerendering, you can't see a difference.