Here's a video of a circuit I made which flashes an LED, using only power collected by the LED:

https://youtube.com/watch?v=BM7VDOoFIWI

The LED is the component on the left; there's a very dim flash (pretty much just the black die turning red) at around 11s, then every few seconds.

I can't remember exactly how it works... I think there's two capacitors charged up to the voltage of the LED in parallel through high-value resistors, and a circuit that shorts the +ve of one to the +ve of the other to put them in parallel.

It only just works at a very specific light level. IIRC some of the transistors are used as very low leakage diodes rather than transistors, as the regular diodes I had we're too leaky.