Imagine you are juggling to a certain rythm, a certain speed, no matter what number you are juggling. If you were to do this, every type of throw would have a distinctly different height and aim. A three-ball throw would be a low toss from one hand to the other. A four-ball throw would be a slightly higher toss that lands in the same hand it is thrown from. A five-ball throw would go slightly higher, and land in the opposite hand. And so on. Thus, you can express a pattern with a series of numbers. A three ball cascade is 333. A four ball pattern is 4444.
A 1 is when you simply pass the ball from hand to hand without it ever being airborne. A two is when you simply hold onto the ball for a beat.
The pattern is separated out into beats. Each beat has a throw with one hand and a catch with the other. A five is caught on the fourth beat after it is thrown. A four lands three beats after it's thrown, and so on.
It gets quite interesting when you have multiple types of throws in the same pattern. For example, 5353 is a four-ball circular pattern (known as a half-shower). 5151 is a three ball shower.
Understanding this concept is very useful when working on four ball patterns, because the throws must all be different and must all be to the right height for many of them to work. Four ball tennis is a very complicated pattern at first, but in siteswap it is fairly easy to describe: 53444. That is, a five is thrown over the top, a three is thrown accross under it, and the next three throws land in the same hand they were thrown from, then you start over.
Patterns loop. In other words, 52233 is the same as 5223352233 or 33522 or 23352, and so on.
Stop reading after this paragraph Above is all you really need to understand to get started. If you don't already have a fairly good grasp of siteswap (and a very good grasp of algebra), the rest of this page will scare the crap out of you. If I haven't explained this clearly enough, try an internet search for "siteswap notation." There are several other sites which give a better description than I do.
SiteSwap can be used to create some patterns, some of which are so complex that they can only be done by a computer. If you want such a program, I reccomend JuggleKrazy, a shareware program that lets you enter a pattern in siteswap notation and watch it done onscreen.
You can go wild creating patterns like this, and be able to figure out whether each one works mathmatically. If you get jugglekrazy, try typing in 63344. The result is a cool looking four-ball pattern where balls seem to randomly pass from hand to hand, and occasionally one ball will explode upwards while the rest of the pattern continues under it. For an even more bizarre pattern, try 63574. This one is beyond description.
In order for a siteswap pattern to work correctly, you must make sure that no two balls come down at the same time. An easy (hah) way to do this is to look at it like a countdown after each throw until it lands. A 5 cannot come on the next beat after a 6. A 4 cannot come the next beat after a 5, and so on. A 4 cannot come on the second beat after a 6, a 3 can't come on the third beat, etc. This is true for any number.
Here's an example. If a pattern starts with 7, it can be followed by anything except a 6, which can be followed by anything except a 5, which can be followed by anything except a four, and so on. But it's more copmlicated then that, because this must hold true for every single throw. For example, if the 7 is followed by a 9, then the next throw can be neither a 5 nor an 8, and the throw after that can be neither a 4 nor a 7.
In other words, if the first throw is (X), the second cannot be (X-1), the third cannot be (X-2), and so on. But his must be applied to every number in the pattern. For an example, I'll use a five digit siteswap (using variables instead of specific numbers.) Our pattern is V W X Y Z. Here's what must be true about each variable:
W cannot equal (V-1)
X cannot equal (V-2), nor can it equal (W-1).
Y cannot equal (V-3), (W-2), or (X-1).
Z cannot equal (V-4), (W-3), (X-2), or (Y-1).
But that's not all. Remember, our pattern loops, so we have to figure out what V can and can't be according to the other four, as well as calculating more requirments for W, X, and Y. In the end, we get these requirements:
V cannot equal: (Z-1), (Y-2), (X-3), (W-4), (Z-5), (Y-6), etc.
W cannot equal: (V-1), (Z-2), (Y-3), (X-4), (V-5), (Z-6), etc.
X cannot equal: (W-1), (V-2), (Z-3), (Y-4), (W-5), (V-6), etc.
Y cannot equal: (X-1), (W-2), (V-3), (Z-4), (X-5), (W-6), etc.
Z cannot equal: (Y-1), (X-2), (W-3), (V-4), (X-5), (W-6), etc.
We can consolidate all of this into a single formula:
For any pattern T1 T2 T3... Tinfinity where Tn is a throw value, there are two required conditions:
1) There must NOT be any throw value Tn such that Tn = (Tn - x) - x.
2) The mean (average) must be a whole number.
3) The average of all the throw values is the number of balls it takes to do the pattern.
Sounds complicated, doesn't it? Don't worry. Eventually, you'll get the hang of it, and it becomes real easy.
