Here's an image I found at about 105 "zooms" (a magnification of 2105 times) into the Mandelbrot Set, using Fractal eXtreme.

utero universalis 250.jpg (13419 bytes)

Utero Universalis - Conal Elliott 1999

Versions: 5K, 14K, 39K, 138K, 377K, and 4.1M.   The last one is truly huge (36 million pixels).  If you print one of the big ones, scale down in the printer settings, and you'll get a high-res printout, rather than just large.  For instance, you may want to scale down to 33% or 25%, or even 10% if you have a high-res (color) printer.  And yes, you'll use a lot of ink, so you might just want to look at them on your computer instead.  You can use Fractal eXtreme to watch this zoom movie (4.8M).  (Right-click on the movie link and choose "Save Target As ...".)

Below is another pretty one.  Here are a big version (1000x1000, 296K) and zoom movie (5.4M) for it.

Fractal Swirls A - Conal Elliott 1999