Here, have a couple of Python scripts. Each creates an image file, 2^12 pixels square, each pixel of a different color.
colorshuffle.py puts the coordinates of each pixel in Gray code, assigns each bit to one of the color channels, and converts each channel back from Gray code to choose a color. The assignment is chosen at random from 141926400 possibilities.
colorfold.py is my attempt to re-create and extend this: it folds the square eight times to make a cube fitting the color space. The interesting part was maintaining continuity through multiple folds. This one has only 107520 possible outcomes; again they’re chosen at random. I don’t like the result nearly as much as the other, but you might!
You’ll need Python Imaging Library.
On my machine each takes less than two minutes, so with a simple shell script you can whip up hundreds overnight.