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# Siteswap state diagrams simplified

This is **juggling theory**.
If you're clueless, go to the
Siteswap help pages
at the
Juggling Information Service,
or to
Siteswap.org,
or to Wikipedia: Siteswap.

## Download printable file

PDF version (180 KB),
DVI version (460 KB).

This document (10 pages) contains nicely typeset simplified siteswap state
diagrams, from which one can read off at a glance all possible vanilla
siteswap patterns for 3 / 4 / 5 ball juggling using throws of height 7 or
less. The diagrams are also very useful for finding transitions between
different siteswaps. Instructions are included, but familiarity with
siteswaps is assumed.

## French version: *Diagrammes d'états et Siteswap*

PDF,
DVI.

This is a translation of the document into French, by Clément Bruneau.

## Sample: 3 ball juggling with throws up to height 5

Here is an image of the smallest nontrivial diagram in the document.
This already includes most well-known 3 ball juggling patterns,
like **3** (cascade), **51** (shower),
**441**, and **531**.
Any loop in the graph gives a valid siteswap, and vice versa.

Double lines represent arrows going in both directions.
For example, to go from the ground state (the box labelled 7/111)
to the shower state (the box labelled 11/1011),
throw **4** or **52**.
To go back,
throw **2** or **530**.

**Technical note**:
The multithrow sequences pass via excited states that
(unless one throws higher than **5**)
have either just one arrow leading in or one arrow leading out.
These states have been eliminated here,
which simplifies the diagrams considerably.
For example,
the **non-simplified** diagram for 3 balls and height 5 has
**ten states** instead of just three;
it can be found in
Section 7 of Allen Knutson's Siteswap FAQ (as ASCII art)
or in
the Wikipedia article about Siteswap (with a better picture).

Original version
2003-01-23.
Last modified
2019-11-29.
Hans Lundmark
(hans.lundmark@liu.se)