The most interesting part of juggling patterns, to me, is how many other kinds of math they are related to. For instance, you can map them to braids in a very interesting way.
If you plotted a juggling routine with time as the 3rd axis, the balls would trace out the braid.
I remember having this realization randomly while doing a standard 3-plait braid (I don't even remember what I was braiding) and realizing I was doing the exact same motion as juggling. Super weird
I wonder how many site swaps make interesting braids. You have some discretion in where the plaits go [inside vs. outside throws, crossing vs. non-crossing simultaneous throws if unspecified], which would help.
