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Theory for popcorns patterns

Author: JiBe
Credits: based on Christophe Pr?chac ideas

7 club popcorn (a definition): a passing pattern in which one juggler lifts 4 clubs, leaving the other one juggling 3 clubs, before he throws back a club and reverse the situation. Similarly, you can define some 8 and 9 club popcorns.

Thanks to Christophe (this pages owes a lot to Christophe and to Hans Gault who discovered these patterns), I understood what were the mathematics (siteswap formulas) behind all these patterns.

You can find some other kind of popcorns (with more than one pass per cycle for instance), but I won't describe them here.


Theoretical part

s s s ... (n times) = {s}n.
Example : {4}3 = 4 4 4

Then it's very short, we simply have the following popcorn families:

2n-count popcorn:
(2n+1)-count popcorn
  • {4}n 3p {3}n-1
  • {4}n-1 4p {3}n

and you can carry on:
{4}n-2 5p {3}n+1

  • {4}n 3.5p {3}n
  • {4}n-1 4.5p {3}n+1

and you can carry on:
{4}n-2 5.5p {3}n+1

You see very well from these formulas there is a 4 clubs part, a pass, and a 3 clubs part.

Remark: All these pattern are symetric, meaning that both jugglers do the same thing (but staggered). We thus only write the sequence of one juggler.


Practical part

When you replace n by some reasonable values, you get quite a few patterns. What is also amazing is to discover here some classical patterns such as the 2-count or the 1-count.

In 2n-count popcorns, the passes are tramline and always made by the same hand.
In (2n+1)-count popcorns, one juggler does crossing passes, the other does straight passes. Juggler 2 starts half a beat after juggler 1, and passes are made from both hands.

Note also that all sequences of 4's can be replaced by an equivalent 4 club siteswap (44 can be replaced by 53, 4444 by 5551, ...). You can do that at any time without warning your partner since it's not going to change anything on their side of the pattern. The same applies to the 3's (333 replaced by 441 or 531).

I've added some stars to indicate the very good ones.

 
2n-count popcorn
(2n+1)-count popcorn
{4}n 3p {3}n-1
{4}n-1 4p {3}n
{4}n 3.5p {3}n
{4}n-1 4.5p {3}n+1
n=0
-
-

3.5p

7 ultimate

-
n=1

4 3p

4p 3

7 clubs 2-count :
normal or crossing

4 3.5p 3

3-count popcorn ***

4.5p 3 3

7 clubs 3-count

n=2

4 4 3p 3

4-count popcorn

4 4p 3 3

 

4 4 3.5p 3 3

5-count popcorn ***

4 4.5p 3 3 3

n=3

4 4 4 3p 3 3

 

4 4 4p 3 3 3

classic popcorn when done with 53.

4 4 4 3.5p 3 3 3

 

4 4 4.5p 3 3 3 3

7-count popcorn

n=4

4 4 4 4 3p 3 3 3

8-count 5551 popcorn ***

4 4 4 4p 3 3 3 3

 

4 4 4 4 3.5p 3 3 3 3

9-count 5551 popcorn

4 4 4 4.5p 3 3 3 3 3