Mandelbulb 3D is a free portable application which generates 3D fractal images. Not the usual 2D Mandelbrots, but 3D objects and scenes which look like they've been plucked from deep space, an alien world or the weirdest dream you've ever had. (If you've never seen them before, take a look at the "Portfolio" page on the Mandelbulb site for some examples.)
The Mandelbulb 3D program is relatively compact (barely 6MB), and doesn't require installation or contain any unwanted extras. Just download and unzip it, view Mandelbulb3DReadme.html for instructions, or run Mandelbulb3D.exe to get started.
If you normally read the manual only in emergencies, then Mandelbulb 3D is going to seem a little intimidating. There are a host of panels, tabs, numbers and checkboxes, and it's not at all obvious how you should begin.
Fortunately it's easier than it looks, at least for basic operations. Clicking "Calculate 3D" generates a 3D fractal from the starting values. Click "Formulas", hover your mouse over one of the formula types (3D, 3Da, 4D etc) and select a new formula for a very different image. Play around with the formula figures to change how it looks, maybe adjust the image size to suit your needs, and save anything you like as an image, ready to share with others.
Alternatively, the Mandelbulb 3D site often displays both sample images and the settings used to produce them, great if you want to get started in a hurry.
It takes a little time to figure out how to get the best results out of Mandelbulb 3D, but your efforts will be rewarded by some amazing fractal imagery.