I'm assuming the source is just ordinary background radiation. I'm wondering if, at such low levels, the geiger counter can accurately determine it enough to get a truly random output (as opposed to, some internal squelch on the unit creating predictable patterns). You probably would get far better randomisation ripping out americium from an old smoke detector and putting it by the geiger counter. (Just take note that residue on your hands from handling it may be toxic if ingested.)