Here's a marriage of Homopolar motor and Joule thief that results in a truly impractical Rube-Goldberg mechanism for blinking an LED with a AAA battery. It may be inefficient, but I like it .. mainly because I haven't seen any quite similar before!
Where did this come from? I stumbled upon the amazing "World's Simplest Electric Train" video posted by 君AmazingScience. After some fiddling around, I ended up with a vertically-mounted demonstration that produced a nice bouncing spring... which immediately got me thinking about the collapsing electromagnetic field on each bounce, and how that reminded me of what is going on in a Joule Thief.
The Design is a simple but novel(?) arrangement of two subsystems:
* AAA battery, magnets and coil are arranged as a bouncy homopolar motor
* a diode and capacitor attached to the coil harvest the flyback energy to power the LED