To me, it would seem that most stims (though maybe not all) seem to have some sort of pattern-creating involved?
Rocking, swinging, looking at patterns, finger drumming, listening to music, pacing, tracing patterns (I trace a figure of eight on my thumbnail, is strange lol), spinning, etc..
Is it some way of calming down a feeling of being out of control or something like that? Seeking some kind of pattern to latch on to?