The above testament to my artistic ability, or specifically my lack thereof, was made in my experiment with digital sculpting, technically, part II. Wikipedia says
Digital sculpting is the use of software that offers tools to push, pull, smooth, grab, pinch or otherwise manipulate a digital object as if it were made of a real-life substance such as clay.
I saw this Lifehacker article on sculptris a few months ago and it sort of made an impression on me of how cool and awesome 3d was. Any real program is of course much different and better than this one because of the ability to actually grab, smooth and pinch the digital object.
You could check out Chaoscope.
Chaoscope, a 3D Strange Attractor rendering freeware
http://www.chaoscope.org/
Also, check out ZBrush, it is really close to digital sculpting and is capable of producing stunning results. It may change your understanding of what 3d design is, too.