# Popcorns I

Credits: Kaskade 69

**See the following part, Popcorns II:
asymmetry, synchronicity and more people
Download a ZIP archive with popcorn
patterns for JoePass!.**

This article is an abbreviated version of extensive exploration of popcorns that we have undertaken over the last couple of years. Although the first popcorns where distinctively club patterns, the patterns described here are worth trying with all the other classic juggling props, and indeed any other that you can think of.

We have taken for granted a basic understanding of siteswaps and less importantly for this article causal diagrams. Causal Diagrams where explained in the last issue of Kaskade (68). If you are unfamiliar with siteswaps I urge you to spend the couple of hours it takes to gain an understanding of them, for they are an invaluable tool in understanding a myriad of wonderfull juggling patterns.

The passing notation we use is Jack Boyce's extension of classical siteswaps. All patterns are given from the perspective of a 2 handed juggler.

Because of lack of space I haven't included most of the charts. I have put them up on our Internet site where you can also find for sale the laminated versions.

## Definition of popcorns.

For the purpose of this article we will define popcorn passing patterns as jugglers taking turns at popping. Popping in this context means lifting into an amount of objects higher than the one they previously had and then throwing the extra things back out. We shall return and be more specific with this definition but for now it should serve us well.

## Classic popcorn

As already thoroughly defined in this column the classic popcorn is <5 3 4p 3 3 3 | 3 3 3 5 3 4p > which since it is symmetrical we can call 5 3 4p 3 3 3

Now for our purposes we want to change the 53 to 44 so as to go from the most simple 4 object pattern to the most simple 3 object pattern. So we get 4 4 4p 3 3 3

Ok so that's a popcorn in its basic state, in this case you juggle 4 for a bit, throw a pass and then juggle 3 for a bit.

## Expanding Popcorns

So now what we want to do is find all the symmetric patterns of the above form that go from 3 to 4 objects. By Symmetric I mean patterns where both jugglers do the same thing, in this case out of time with each other.

The chart below is the expansion:

Horizontally we expand by adding a 3 on one side of the pass and a 4 on the other. This means that each step along the chart gives each juggler an extra throw of the 2 solo patterns. | |

Vertically we expand by adding and removing 3s by increasing and decreasing the pass by half a beat. So for example in club juggling decreasing the pass from a 4 to a 3.5 means doing a floaty single instead of a normal double. |

**7 objects popcorn chart**

5.5p3333 | 45.5p33333 | 445.5p333333 |
4445.5p3333333 | 44445.5p33333333 | 444445.5p333333333 |

5p333 | 45p3333 | 445p33333 |
4445p333333 | 44445p3333333 | 444445p33333333 |

4.5p33 | 44.5p333 | 444.5p3333 |
4444.5p33333 | 44444.5p333333 | 444444.5p3333333 |

4p3 | 44p33 | 444p333 |
4444p3333 | 44444p33333 | 444444p333333 |

3.5p | 43.5p3 | 443.5p33 |
4443.5p333 | 44443.5p3333 | 444443.5p33333 |

43p | 443p3 |
4443p33 | 44443p333 | 444443p3333 | |

442.5p |
4442.5p3 | 44442.5p33 | 444442.5p333 | ||

4442p | 44442p3 | 444442p33 | |||

44441.5p | 444441.5p3 | ||||

444441p3 |

The chart expands to infinity upwards and to the right

There are a lot of fun patterns here! Over the last year we have juggled most of them. The lower extremities tend to be the hardest. Our problems started with the 2.5 passes. In principle these are faster than an ordinary 3. We got round it by really slowing down our 4s. I initially included the 1ps,1.5ps and 2ps for aesthetic reasons but have realised that one can turn them into interesting patterns by giving the club, as opposed to passing it.

Notice interestingly that the patterns on the column furthest to the left, 3.5p, 4p3, 4.5p33, 5p333, 5.5p3333 are the usual 7 objects 1-count, 2-count, 3-count, 4-count and 5-count respectively. Here we encounter our first dilemma since each juggler lifts into the new amount of objects for 0 beats. Are they popcorns?

For a more thorough understanding of the popcorn progression it might help to look at the causal diagram chart for the seven object chart. Sometimes diagrams can speak more than words or numbers.

## More Objects

So now lets look at 8 object popcorns.

There is a chart where both jugglers do the same thing in time with each other, patterns like 46p33, however for now we will concentrate on patterns where the jugglers are symmetrically staggered in time. This means both jugglers do the same thing at different times.

So the staggered chart has 2 passes, each juggler lifting from 3 objects to 5 objects.

5.5p5.5p333 | 55.5p5.5p3333 | 555.5p5.5p33333 |
5555.5p5.5p333333 | 55555.5p5.5p3333333 | 555555.5p5.5p33333333 |

5p5p33 | 55p5p333 | 555p5p3333 |
5555p5p33333 | 55555p5p333333 | 555555p5p3333333 |

4.5p4.53p | 54.5p4.5p33 | 554.5p4.5p333 |
5554.55p4.5p3333 | 55554.55p4.5p33333 | 555554.55p4.5p333333 |

4p4p | 54p4p3 | 554p4p33 |
5554p4p333 | 55554p4p3333 | 555554p4p33333 |

53.5p3.5p | 553.5p3.5p3 |
5553.5p3.5p33 | 55553.5p3.5p333 | 555553.5p3.5p3333 | |

553p3p | 5553p3p3 |
55553p3p33 | 555553p3p333 |

We started learning the patterns above with rings so as not to have to deal with spin. The ones we found easiest to start with where the longer versions of ……4p4p….. With these you have time to steady your 5 object pattern before having to throw out. However if you find five difficult perhaps the shorter patterns are easier. With clubs we started with 54p4p3 with the 5 a triple and the 4s doubles. We also do the above long pass with the fives as doubles.

So back to the charts, here are the two 9 object charts In the first chart
each juggler alternates between 4 and 5 object patterns while in the second
it is between 3 and 6 object patterns.

**9 objects 1 pass**

6.5p4444 | 56.5p44444 | 556.5p444444 |
5556.5p4444444 | 55556.5p44444444 | 555556.5p444444444 |

6p444 | 56p4444 | 556p44444 |
5556p444444 | 55556p4444444 | 555556p44444444 |

5.5p44 | 55.5p444 | 555.5p4444 |
5555.5p44444 | 55555.5p444444 | 555555.5p4444444 |

5p4 | 55p44 | 555p444 |
5555p4444 | 55555p44444 | 555555p444444 |

4.5p | 54.5p4 | 554.5p44 |
5554.5p444 | 55554.5p4444 | 555554.5p44444 |

54p | 554p4 |
5554p44 | 55554p444 | 555554p4444 | |

553.5p |
5553.5p4 | 55553.5p44 | 555553.5p444 | ||

5553p | 55553p4 | 555553p44 |

**9 objects 3 passes**

6.5p6.5p6.5p3333 | 66.5p6.5p6.5p33333 | 666.5p6.5p6.5p333333 | 6666.5p6.5p6.5p3333333 | 66666.5p6.5p6.5p33333333 |

6p6p6p333 | 66p6p6p3333 | 666p6p6p33333 | 6666p6p6p333333 | 66666p6p6p3333333 |

5.5p5.5p5.5p33 | 65.5p5.5p5.5p333 | 665.5p5.5p5.5p3333 | 6665.5p5.5p5.5p33333 | 66665.5p5.5p5.5p333333 |

5p5p5p3 | 65p5p5p33 | 665p5p5p333 | 6665p5p5p3333 | 66665p5p5p33333 |

4.5p4.5p4.5p | 64.5p4.5p4.5p3 | 664.5p4.5p4.5p33 | 6664.5p4.5p4.5p333 | 66664.5p4.5p4.5p3333 |

64p4p4p | 664p4p4p3 | 6664p4p4p33 | 66664p4p4p333 | |

663.5p3.5p3.5p | 6663.5p3.5p3.5p3 | 66663.5p3.5p3.5p33 | ||

6663p3p3p | 66663p3p3p3 |

We haven't yet managed the 3 pass versions with clubs. I would love to see them!

Notice that for now we are just listing popcorns where the lowest amount of objects juggled is 3. There are however popcorns which go from 2 objects to 4 objects, from 0 to 6 or indeed any combination that you care to think of!

## Siteswap syncopations

Earlier we changed the classic popcorn from 53 to 44. We can now do the opposite and replace any series of throws by their siteswap equivalent. So for example classic popcorn has 3 selfs (siteswap 3) throws which we can replace by any period 3 siteswap. Ie 522, 441, 531, 342…

The other fun thing one can do is synchopate the passes as well. So for example 334p4p55 can become 335p3p55!

And last but not least you can apply the principle of late and early passes that one does in 4 count passing. So in classic popcorn 444p333 one of the jugglers can do 45p3333. In club passing this could be a crossing triple pass.

## In Conclusion

Up to now we have only considered patterns that leave ground state and return to ground state. There are off course a whole family of patterns where this is not the case. For example one can draw up the chart of popcorns that go from 3 shower to 4 shower. The problem is that we cannot do this without transition throws. The resulting patterns are very interesting but lack the qualities that I would call popcorn. To clarify I would redefine popcorns as going from ground state to ground state. This implies that contrary to what one might think not all passing patterns are popcorns. Next article we will look more in detail at what we mean as ground state as well as all kinds of hybrid popcorns.

I hope that you will find some interesting patterns to play with in the ideas above.

Thanks for Wolfgang Westerboer, JiBe and Jon Skjerning-Rasmussen for their help writing this article.

**See the following part, Popcorns
II: asymmetry, synchronicity and more people
Download a ZIP archive with popcorn
patterns for JoePass!.**

### Bibliography

An extended version of this article including all the charts can be found at
www.gandinijuggling.com

Jack Boyce's passing notation http://juggleanim.sourceforge.net/doc/notation.html

Christophe Prechac's extremely technical but very interesting pages, See particularly
his article on generating all symmetric passing patterns from 2 handed siteswaps.
http://pogo5.free.fr/juggling/mhn&causal.html

Wolfgang Westerboers fantastic passing animator http://www.koelnvention.de/software/index.html