Re: juggling's combinatorics problem with siteswap

From: Xah Lee (xah_at_xahlee.org)
Date: 02/13/05 

Date: 13 Feb 2005 14:01:53 -0800

Thanks Owen for suggestions and correction...

some more sketches and ideas...

* siteswap notation is a sequence of numbers, as in {5,3,4,4,4} (4
balls tennis pattern). If each number is single digits, then it can be
abbreviated to 53444.

* length of sitewap is the number of numbers in it. i.e.
length[53444]==5.

* bs = number of balls.

* cp = a colored period is the number of throws all colored balls
return to their position. For example, for pattern 53444, the cp is 30.

* ucp = uncolored period. The number of throws all uncolored balls
return to their position. In 53444, ucp = 10.

* rucp = reduced uncolored period. Like ucp, but consider mirror images
are excluded. rucp for 53444 is 5. (rucp is the unmber of digts in
siteswap.).

* obs = the number of orbits in a pattern. (a orbit is the path a ball
travels.) In 53444, obs = 2. (note: each orbit can have its own cp,
ucp, rucp and siteswap notation.)

* amb = true if ambidextrous, ortherwise false. A pattern is
ambidextrous if left and right hand play the same role. (if length of
siteswap is odd, then ambi is true for sure. 8448 is a counter example.
It is ambidextrous.)

I haven't studied the siteswap notation much... will have to spent time
on it. And, some of the algorithms and examples suggested here should
be incorporated...

some of the above idea also needs to be refined. For example, in Steve
Bennett's 8448 example, although it is ambidextrous but note some balls
never goes to the other hand. i.e. the obits are single node loops, but
the whole pattern does contain balls that change hands.

here's some interesting siteswap patterns i've jotted down in my
notes...

* 3 ball on one hand, 2 on the other. (64)
* 3 balls snake (55050, 7070700)
* single handed 3 balls (60)
* continuous 3 balls flash (55500, 7770000)
* 4 balls tennis (53444);
* 4 balls shower. (71)
* 3 balls shower (51)
* 2 balls shower (31)
* 4 balls cascade (55550)

 Xah
 xah@xahlee.org
 http://xahlee.org/PageTwo_dir/more.html

owenjonesuk wrote:
> I have recently done some research into the history of siteswap and I

> found a multitude of papers on the internet. Probably the best source
is
> the Mathematics of Juggling by Burkard Polster. I haven't read it,
but
> several people who have and a very good review online all say that it
is
> completely aimed at mathematical audience and that it has a great
list
> of references.
>
> Owen
>
> PS Siteswap was devised in 1984 or 85, although it didn't take off in

> popularity for a while.

Relevant Pages

  • Re: 3 Ball Juggling Blog
    ... more balls, or perhaps just more complicated looking variations. ... tricks with applied pattern notation? ... This applies to any siteswap, ...
    (rec.juggling)
  • Re: numbers of siteswaps
    ... The code in question is in fact '534' but changed from four balls, ... distinct siteswap, since '53034' and '53403' are digit-shifts for the ... people coming into juggling, such as 'GoldenJ' and MichaelB, have the ... are not really juggling and certainly are not becoming "a juggler". ...
    (rec.juggling)
  • Re: jugglings combinatorics problem with siteswap
    ... (4 balls tennis pattern) ... And siteswap always mean canonical siteswap ... ... For example, for pattern 53444, the cp is 30. ... * obs = the number of orbits in a pattern. ...
    (sci.math)
  • Re: [math] labeled ball juggling
    ... A proper siteswap is not a repetition of any shorter siteswap. ... An unstacked siteswap has as many orbits as there are balls; ... The length of the unstacked repetition ... A labrime siteswap is an unstacked siteswap ...
    (rec.juggling)
  • Re: Learning to Juggle a Period 4 Mills Mess
    ... I'd like to learn to juggle a period 4 siteswap with a Mills Mess hand ... What is a good period 4 pattern with 3 balls to try? ... So for 342 millsmess, starting with your arms ... If you meant millsmess with a siteswap of period four, ...
    (rec.juggling)