What I find fascinating is how there's a whole mathematical formalism for describing juggling patterns called siteswap which allows patterns to not only be described, but discovered. It's based on throw heights, with the basic 3-ball cascade being represented by 3 - a sequence of balls thrown so they land 3 beats later on, repeated indefinitely. 531 indicates one ball thrown high, one mid-height and then one passed directly across from one hand to the other.
Much more in-depth treatment here including synchronous and multiplex patterns, ladder and causal diagrams and a bunch of proofs relating to the notation:
Basic intro:
http://www.twjc.co.uk/siteswap.html
Much more in-depth treatment here including synchronous and multiplex patterns, ladder and causal diagrams and a bunch of proofs relating to the notation:
https://www.jugglingedge.com/pdf/BenBeeversGuidetoJugglingPa...
but you can always go here and try a few patterns such as 3, 441, 531, 504, (4,4) or in windmill/Mill's Mess mode, 423
http://www.gunswap.co/