Fun with Multiplexes

The multiplex is common knowledge among the juggling community. Used as a fancy start for a routine, a photo-opportunity (1-up 4-up anyone?) or for a quick bail-out after a bad catch, many jugglers have mastered one or two multiplex tricks. Due to all the possible combinations of throws in a multiplex, the variation in these types of tricks can become very large. I will attempt to outline some of these different groups or styles of patterns, from the very easy to the technically complex. Hopefully this will give you some inspiration to go out and explore this, an in my opinion, often undervalued family of tricks.

The “Splits”

One of the most commonly used multiplexes is where two (or more) balls are thrown from one hand and split over the two hands. In siteswap notation the most standard are the [43] and the [54]. Personally, I find the [54] to be a bit easier, since it feels counter intuitive to throw the ball that goes straight up higher than the one that crosses. But I can imagine that preferences vary. Both are indicated in the following figure.

Lots of different patterns exist with these splits. Some basic examples with four balls are [43]23, [54]21 and [54]6122. A relatively simple and nice pattern with five balls is [54]24. Of course you can expand on these with multiplex throws like [65], [74] or even [83] if you want. However, this could result in patterns with a higher total of balls and a higher complexity. In the case of [83], it will also be very challenging to throw it correctly within a running pattern. Another interesting split is [4×4]. It is like [43], but the balls stay at the same height:

This multiplex only works (mathematically that is) in synchronous patterns. It is often used in a style of juggling named ‘Claymotion’. This style was developed by Richard Clay in the 90’s, and consists of a starting-stopping style, making use of this [4×4] multiplex in a lot of its basic 3 ball patterns. You can find all the basic information on claymotionjuggling.com, with a short tutorial here:

When researching Claymotion for a juggling class, I also came across this video of the IJA Chairman Nathan Wakefield for the 2012 IJA Video Tutorial contest (there’s also a part 2 on his channel).

I haven’t seen a lot of Claymotion videos recently (only 2 in 2014 after a quick youtube search), so I think there is still some undiscovered ground there.

The “Stacks”

Logically, next to the splitting multiplexes, there are those throws where the numbers are all even or all uneven. Both balls stay in one vertical line, the so called ‘stack’. These are most simply noted in siteswap as [53] (crossing) or [64] (not crossing), with possible patterns like [64]23 or [53]25, both with five balls.

This gives already way to a lot of possibilities, however often overlooked are those patterns where the same number is used twice. A good example for this is [33], a six ball pattern that looks like this (in mills’ mess):

Even more impressive, Alexandr Koblikov manages to juggle [55] (with a pirouette):

In siteswap these balls are supposed to be thrown as a bundle against each other. However, in reality it shows that these are easiest when thrown as a stack.
The examples above are however only the basic patterns. Within siteswap, there are also some other possibilities. Firstly, you can change every throw in a siteswap pattern by their corresponding multiplex double. For example, if you take 441, you can change it into [44][44][11]. Some other examples like [77][55][33][11] or [55][33][44] are displayed in this video by Matthew Tiffany:

A second possibility is with throws that are the same as (or can be divided by) the period of the pattern.  Because these throws keep following the same path over and over in the pattern, you can change these for their multiplex double as well. For example, pattern 531 has a 3 in it that goes back and forth with the two other balls switch positions between the 5 and the 1 around it. That means you can change it to 5[33]1, which is an interesting four ball pattern. Other examples are 5[33]4, [66]42 or even 97[55]31.
This same rule also applies to throws that are already multiplexes, for example the pattern [43]23 can become [433]23. It can also become [43]2[33] of course, or [433]2[33], which looks like a right mess. Some playing around with software like Juggling Lab shows that there are some interesting patterns to be found like this.
Another interesting one is the [11], with a group of patterns based on it called ‘shower implosions’, from this old video by Dan Marden:

These start out easy, but become very difficult indeed. Another esthetically pleasing way to juggle these throws is by keeping them flat towards the audience, shown here in a box pattern by Ryohei Kimura:

The “Holds”

Holding a ball and waiting for another is more or less key within the multiplex throws. Most of the standard multiplex patterns include a ‘2’ to wait for the second ball and build up the multiplex. However, a 2 in a multiplex throw has some interesting features. Of course, you can make it into an active 2, which makes it a part of a split or a stack, depending on the other throw. Or use the time with the 2 for an additional manipulation move. But another possibility arises when you decide to hold it. If you look at the pattern [32] for example, you juggle three balls, while holding two additional balls in your hands. However, there is nothing indicating which ball you actually have to throw. This gives some possibilities towards color changing patterns or other visually interesting stuff, although this hasn’t really been explored.

The “Impossibles”

This is a name I made up when first trying these types of patterns. But don’t be fooled, they are very much possible. These are the multiplexes where a 1 (passing a ball) is combined with an actual throw. For example [31] is a throw where you throw one ball to the other hand while passing one to that same hand. Even more challenging is a [41] where one ball is passed and the other goes straight up:

When running these in a simulator, they look pretty impossible, however they can be done when the receiving hand for the passed ball is brought into the path of the throw. So it takes some trial and error with hand positions, but it works out. The Siteswap DVD has a very interesting section with Samuli Mannistö, called Multiplexes for the Masses, where he starts off with some of these patterns going from very easy to the mind-boggling complex.

Expansions

Not really new types of multiplex throws, but some final notes I wanted to add:

Sprung multiplexes

This is another name I came up with, but there are probably other names used. Here the rhythm of the hands within a pattern is broken up to throw both throws of multiplex not together, but in quick succession. This messes up the rhythm, so it takes some practice to make it all fit within the space of the pattern, but theoretically this can be done with any multiplex.

I first came across these patterns when watching Throw Joy by Wes Peden. For example, in his latest 6 clubs video, this a [33] pattern with the throws in quick succession:

There are some others spread throughout Throw Joy, and at first glance it’s always very difficult to make out what is actually happening due to the abnormal rhythm.

Squeezes

As also mentioned in my previous article, a reverse multiplex or a ‘squeeze’ is when two balls are caught in the same hand at the same time. This means that every squeeze pattern needs to have a multiplex in it, in order to keep it going. Combining both multiplex throws and squeezes results in some very tricky patterns, as for example all the period one multiplex patterns like [31],  [43] or [64]. All these multiplexes have to land in a squeeze catch as well, without a held ball. These patterns are mathematically very possible, but prove almost impossible to juggle in real life.

More than two

Most of my examples have been dealing with two ball multiplexes. Of course all of this is also applicable to three ball multiplexes or even more (triplexes, quadplexes and the like), and of course also to clubs and rings. This just goes to show how much there is still to be tried with multiplexes and how much there is still to be discovered.

So go out and explore!

sources:

https://jugglesensei.net/MultiplexWorkshop.pdf

www.claymotionjuggling.com

Hans Nickmans

Hans, a Belgian juggler, started out with diabolo in 2003. Shortly after he taught himself how to juggle three balls and never stopped juggling since. He has a strong interest for juggling theory and recently started teaching juggling at a local circus school.