Ladder diagram

A ladder diagram is a 2-dimensional visual representation of a juggling pattern. The first people known to have used ladder diagrams to notate juggling patterns are Claude Shannon and Jeff Walker, both in the early 1980s.
The vertical dimension of the diagram represents time, and it is conventionally drawn so that going down the ladder corresponds to going forward in time, with the "rungs" of the ladder separating evenly spaced beats in the pattern. (The ladder diagrams that Juggling Lab creates don't show the rungs.) Turning a ladder diagram of a pattern upside-down turns it into a diagram of the time-reversed version of the pattern.
The lines going down the ladder represent the paths that the props take through time and space (ignoring the vertical dimension of physical patterns). The number of paths that intersect a horizontal line anywhere in the diagram is the number of props in the pattern. Throws and catches made with the right or left hand are shown on the corresponding side of the diagram.
This is a ladder diagram of the 3 ball cascade. The throws are made alternately from the right and left sides. Every throw crosses to the other side of the pattern, and is thrown again three beats later. No dwell time is shown in this diagram.	
This is another diagram of the same pattern, showing one beat of dwell time per throw, so that each throw has two beats of air time and then is held for one beat before it's thrown again. Each prop is still thrown every three beats. Each hand is alternately empty for one beat, and full for one beat.
When dwell time is shown in a ladder diagram, the throws and catches are drawn separately. The empty circles represent throws, and the filled circles represent catches.	
The diagram of 531 has lines of three different lengths, corresponding to the different throw heights.
The siteswap value of each throw is the number of rungs the line goes down the ladder before the ball is thrown again.
In the diagram of 423, the odd number throws are straight lines that cross to the other side of the diagram, and the even number throws stay on the same side. Even number throws higher than 2 have to be drawn as curved lines to make the diagram readable.
A 2 is drawn as a short vertical line representing a prop that is held for two beats before it's thrown again. (If dwell time was shown in the diagram, a 2 would be an object held for two beats longer than the usual dwell time.)	
In 504, a 0 is an empty beat, where no props are thrown or caught.	
This diagram shows transitions between an asynch fountain and a synch fountain with 4 balls. The first throw that is different from the asynch fountain (the 5th beat from the top) is a non-crossing 5 (written as 5x), followed by a 4, and then a one beat hold (a 1x in siteswap) before the synch pattern starts.
...4444 5x41x (4,4)(4,4)...
The synch fountain alternates between a beat where two 4s are thrown at once, and an empty beat (a beat with no throws). The first beat of the transition from the synch fountain (the 8th beat from the bottom) contains a non-crossing 5 (a 5x) from the right, and in the next "synch pair" only one ball is actually thrown, and the other is held for one beat (a 1x). The asynch fountain starts immediately after this - an exclamation mark in the siteswap indicates that that pair of "throws" is not followed by the usual empty beat.
...(4,4)(4,4) (4,5x)(4,1x)! 4444...
Category:Notation