Siteswap - Vanilla Siteswap

Vanilla Siteswap

Its simplest form, sometimes called vanilla siteswap, describes only patterns whose throws alternate hands and in which one ball is thrown at a time. If we were to watch someone from above as they were juggling while walking forward, we might see something like the diagram to the right, which is sometimes called a space-time diagram.

We can describe this pattern by stating how many throws later the ball is thrown again. For instance, on the first throw in the diagram, the purple ball is thrown in the air by the right hand, next the blue ball, the green ball, the green ball again, and the blue ball again and then finally the purple ball is caught and thrown by the left hand on the fifth throw, this gives the first throw a count of 5. We end up with a sequence of numbers which denote the height of each throw to be made. Since hands alternate, odd-numbered throws send the ball to the other hand, while even-numbered throws send the ball to the same hand. A 3 represents a throw to the opposite hand at the height of the basic three-cascade; a 4 represents a throw to the same hand at the height of the four-fountain, and so on.

There are three special throws: a 0 is a pause with an empty hand, a 1 is a quick pass straight across to the other hand, and a 2 is a momentary hold of an object. Throws longer than 9 beats are given letters starting with a. The number of beats a ball is in the air usually corresponds to how high it was thrown, so many people refer to the numbers as heights, but this is not technically correct; all that matters is the number of beats in the air, not how high it is thrown. For example, bouncing a ball takes longer than a throw in the air to the same height, and so can be a higher siteswap value while being a lower throw.

Each pattern repeats after a certain number of throws, called the period of the pattern. The pattern is named after the shortest repeating segment of the sequence, so the pattern diagrammed on the right is 53145305520 and has a period of 11. If the period is an odd number, like this one, then each time you repeat the sequence you're starting with the other hand, and the pattern is said to be symmetrical because each hand is doing the same thing (although at different times). If the period is an even number then on every repeat of the pattern, each hand does the same thing it did last time and the pattern is possibly asymmetrical because each hand might be doing something different.

The number of balls used for the pattern is the average of the throw numbers the pattern. For example 441 is a three-object pattern because (4+4+1)/3 is 3, and 86 is a seven-object pattern. All patterns must therefore have a siteswap sequence that averages to an integer. Not all such sequences describe patterns; for example 543 with integer average 4 but its three throws all land at the same time, colliding.

Some hold to a convention in that a siteswap is written with its highest numbers first. One drawback to doing so is evident in the pattern 51414, a 3-ball pattern which cannot be inserted into the middle of a string of 3-throws, unlike its rotation 45141 which can.