thumb|Siteswap beats shown as relative height

Siteswap, also called quantum juggling or the Cambridge notation, is a numeric juggling notation used to describe or represent juggling patterns. The term may also be used to describe siteswap patterns, possible patterns transcribed using siteswap. Throws are represented by non-negative integers that specify the number of beats in the future when the object is thrown again: "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."

For example, a three-ball cascade may be notated "3", while a shower may be notated "5 1"._n</math>). One presentation of this group is as the set of bijective functions f on the integers such that, for a fixed n: f(i + n) = f(i) + n for all integers i. If the element f satisfies the further condition that f(i) ≥ i for all i, then f corresponds to the (infinitely repeated) siteswap pattern whose ith number is f(i) &minus; i: that is, the ball thrown at time i will land at time f(i).

Connections to topology

A subset of these siteswap patterns naturally label strata in the positroid stratification of the Grassmannian.

List of symbols

  • Number: Relative duration (height) of a toss. 1, 2, 3...
  • Brackets []: Multiplex. [333]33.
  • Chevrons and vertical bar <|>: Simultaneous and passing patterns.
  • P: Pass. <333P|333P>
  • Fraction: Pass 1/y beats later. <4.5 3 3 | 3 4 3.5>
  • Parentheses (): Synchronous pattern.
  • *: Synchronous pattern that switches sides. (4,2x)(2x,4) = (4,2x)*
  • x: Toss to the other hand during a synchronous pattern.

See also

  • List of siteswaps

Notes

References

Further reading

  • <!--called "the most comprehensive resource," by Erik R. Tou, ISBN 9781400873371.-->
  • "Symmetric Passing Patterns", PassingDB.com.
  • DSSS: The Diabolo Siteswap Simulator, ArtofDiabolo.com.
  • Juggling Lab (Downloadable animator)
  • Gunswap Juggling (Online animator)
  • TWJC Siteswap Calculator (Helpful Vanilla, Multiplex and Synchronous siteswap validator)
  • "Staggered Symmetric Passing Patterns for 2 jugglers" by Sean Gandini (social siteswaps)