Three coils would be prohibitively expensive. I intend to produce quite a few of these units once I have a working prototype so the fewer components the better. Having given it some more thought I prefer the random approach out of the two options, also reversing the polarity of the coil should avoid those pesky dead spots, plus I think I'd only need one coil.Hmmm. I can see from the link that the random option would be more versatile. For that option I'm now wondering if perhaps you might need 3 coils to guarantee the movement you want?
Nick