Over at SpriteMods, [sprite_tm] realized that a microcontroller could be used as a boost converter to power itself. A boost converter steps up voltage from a battery by switching the output of a coil.
To wrap up the build, he added a 2000mAh 3.7V Li-Ion battery and TP4056 charger, with a DC-DC boost converter to get 5V for the Arduino. Though if you wanted to create a benchtop version of this ...