Then, when you figure out that a certain set of patterns are jugglable, you try to figure out state diagrams for things like "What are all the possible rhythms for juggling three objects, under some maximum number of beats in the air?" [2]
I've definitely caught myself idly drawing ladder diagrams[3] before, then plugging the mathematical results into Juggling Lab[4] to see what it would look like, e.g. [5]. :)
[1] https://www.youtube.com/watch?v=X1zSlvQtKM4
[2] https://plus.maths.org/issue52/features/polster/state1.jpg
[3] https://vignette4.wikia.nocookie.net/juggle/images/b/ba/0123...
[4] http://jugglinglab.sourceforge.net
[5] https://vignette.wikia.nocookie.net/juggle/images/8/8f/86x4x...