atypical LED display

I'm doing an art project, and I'm trying to create the illusion of motion by using LEDs.* I don't know where to begin.  The illusion involves two groups (G1, G2) of LEDs (three) acting in relation to one another. I'll try to just flow chart it:

1. Power on

2. G1 fades up over a period of one minute, almost imperceptible.

3. Ten minutes later (or at random periods of 5-15 minutes), G1 fades off over a period of one second. This might also be known as instant off.

4. Immediately thereafter, G2 fades up over a period of one to two seconds--or instant on. 

5. G2 stays on for two minutes

6. G2 fades off for one minute

7. repeat

The illusion of motion is caused by the quick movement of light (steps 3, 4) from one source to another. I haven't decided whether fast-fade-down, fast-fade-up or instant-off, instant-on would convey the illusion of motion better. It seems like a simultaneous fast-fade-down, fast-fade-up (1-2 seconds) might work best, but I don't know. It's something I'd have to see to decide.  Unless someone already knows.

Any ideas?

This circuit will be in proximity to a full-on string of 30 tiny LEDs; thus, it can pull power from that circuit if necessary (I'm guessing it can).

*The LED's I'm using don't have a size indicated on the box, but I can tell you each is smaller than the head of a pin. Like not even one mm wide.