Manipulation of symbolic notation can lead to new knowledge.

In 1985, there arose independently and almost simultaneously in at least three different places a notation for a limited type of juggling. Making some assumptions about the style employed it was discovered that juggling patterns could be described by sequences of numbers, and that these sequences themselves fell in patterns. By using these patterns of patterns, new juggling patterns were discovered/invented.

Example:

  ...    4 4 4  4  4 4 4 ...
  ...   4 4 4  5 3  4 4 4 ...
  ...  4 4 4  5 5 2  4 4 4 ...
  ... 4 4 4  5 5 5 1  4 4 4 ...
These are all juggling patterns. Without knowing any more, can you deduce the existence of another? If so, and if you're right, then without knowing anything special about juggling you have just discovered a juggling pattern.

For those who haven't guessed, siteswap is read as follows: Each number is a throw. The throws alternate between the left and right hands. The number is how many throws later the object will be thrown next; the time spent in the air will be approximately one half to one beat less than the throw 'value'. 2s are usually read as a 'hold', and 0s are beats when a hand is empty.

Since its creation in the 80s (and especially in the last 10 years), siteswap has been extended in different directions by different parties, several of them programmers of juggling pattern animators. Most of the major variants are somehow related to passing (patterns with more than one juggler), which siteswap does not directly approach.

Some of the major variants are:

* Synchronous siteswap, e.g. (6x,4x) or (2x,4)(4x,2x)* - Each pair of numbers represents two throws, one from each hand. Common for describing 2-ball patterns.
* Synchronous siteswap, examples too long to show. Used by JugglingLab.
* Passing siteswap, e.g. <3p 3 3 | 3p 3 3>  - Each of the lists separated by bars is for a different juggler for passing patterns. Provided by PassingDB and accepted by JoePass!
* 4-hand siteswap, e.g. 966 - A special case for two-person patterns where all four hands throw in order, out of sync. Passes between the two jugglers at a given height will be straight across for one juggler, and diagonal for another! Used by PassingDB and other sources.
* MHN and Beatmap - Not specifically called variations on siteswap, but derivative.