I've seen low-budget backdrops at concerts/performances which were merely a few LEDs sporadically placed about a dark curtain, emulating what could be stars - having just a simple flashing & flickering pattern. I see these and think to myself; I can totally make that in a jiffy!
I never had the motivation to actually go about it until recently: Someone I had met at an event had contacted me wondering if I could build such a thing for a benefit dinner event. The request was for a large 14ft x 8ft backdrop that would be emulating burning embers. Perfect, that's exactly like the starry curtains do with white LEDs. To be flame-like, I'd use red LEDs at the bottom, gradually using orange LEDs in the middle, finishing with yellow LEDs at the top.
Cool! Easy. I don't want to bother with programming or microcontrollers with this, so to get some flickering I thought of using LEDs from electronic tea-light candles. Also, it would be nice to have a lapping flame effect, I used what is called a shift register to take the flicker of a tea-light LED and "shift" it through 8 distinct sections of LEDs. That ended up working great, the backdrop has a flowing animation upward, while each distinct group of LEDs has its own flickering effect as well.