I was introduced to 3D fractals a few years ago via the iPad and iPhone app, Mandelbulb HD, by Angisoft. These apps enable the user to explore the fractal geometry of the mandelbulb. It has often struck me that exploring this fractal landscape is akin to hiking through a national park and photographing the sights.
The iPad app is somewhat limited by the processing power of the iPad itself. To this end, I discovered Mandelbulb 3D (MB3D). MB3D is written for Windows, but can also run on OS X and Unix without having Windows installed, thanks to WINE, a compatibility layer that duplicates the functions of Windows. MB3D is capable of much higher resolution rendering than the iPad app, which is necessary to achieve high quality imagery.
Below are some recent renderings I've done while exploring "Fractal National Park". Be sure to click on the images to get a high rez view.
The amount of variation found within the mandelbulb—which is nothing more than a mathematical formula visualized with computer graphics—is nothing short of mind-blowing. And this is only one formula, many of which that can be explored.
Using MB3D, you can even hybridize various formulae to synthesize new worlds to explore. Imagine taking Rocky Mountain National Park and hybridizing it with Grand Canyon National Park. You'd end up with a new national park that exhibits features of both!
I have a feeling I'll be hiking through these parks for some time to come.