Siteswap

Siteswap is a juggling notation used to describe or represent juggling patterns. Siteswap may also be used to describe siteswap patterns, possible patterns transcribed using siteswap. It encodes the number of beats of each throw, which is related to their relative height, and the hand to which the throw is to be made: "The idea behind siteswap is to keep track of the order that balls are thrown and caught, and _only_ that." It is an invaluable tool in determining which combinations of throws yield valid juggling patterns for a given number of objects, and has led to previously unknown patterns (such as 441). However, it does not describe body movements such as behind-the-back and under-the-leg. Siteswap assumes that, "throws happen on beats that are equally spaced in time." Throws are represented, "by [positive] integers that specify the number of beats in the future when the object is thrown again."

The numbers are as follows:

For example, a three-ball cascade may be notated "3", while a shower may be notated "5 1". The height, and thus difficulty, of throws increases exponentially and siteswaps above 5 are rare except in numbers juggling. The name siteswap comes from the ability to generate patterns from "swapping" numbers in preexisting patterns, such as 55500 and 50505 (or Flash and Snake).

The notation was invented by Paul Klimek in Santa Cruz, California in 1981, and later developed by undergraduates Bruce "Boppo" Tiemann and the late Bengt Magnusson at the California Institute of Technology in 1985, and by Mike Day, mathematician Colin Wright, and mathematician Adam Chalcraft in Cambridge, England in 1985 (whence comes the alternative name). The numbers derive from the number of balls used in the most common juggling patterns. Siteswap has been described as, "perhaps the most popular".

Its simplest form, sometimes called vanilla siteswap, describes only patterns whose throws alternate hands and in which one ball is thrown at a time. If we were to watch someone from above as they were juggling while walking forward, we might see something like the adjacent diagram, which is sometimes called a space-time diagram or ladder diagram. In this diagram, time progresses from the top to the bottom.

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