Pretzel Hand – A Juggling Notation

Version 1.5

– Contents

– Introduction
– What is Mills Mess?
– The Eight Base Patterns
– Sebs Mess
– Learning Patterns with Pretzel Hand
– Butterfly Messes
– Hectic Messes
– Siteswaps
– Mills Mess Variations
– Acknowledgements
– Appendix A: List of Patterns
– Appendix B: Building Ingenious Messes From Hulking Windmills
– Appendix C: Random Pretzel Hand Theory
       – Time Reversing a Pattern
       – Pattern Identification
       – Outside Mills/Flos Transformations
       – Have we found all the 3:3 Messes?
       – How many Rubenstein’s Revenges are there?

– Introduction

This is a notation that I’ve started using to help me learn some mills mess variations. It describes the position the arms are in when throwing and catching. I also use it to work out the pairs of throws and catches with two objects that can be used to learn the mills variations. It mainly utilises the following letters and symbols:

R – right arm on top throw
L – left arm on top throw
U – arms uncrossed throw
r – right arm on top catch
l – left arm on top catch
u – arms uncrossed catch
o – all outside throws (from outside of pattern to the center)
i – all inside throws (from center of pattern to the outside)
/ or \ – which side of the body the first throw peaks on
: – change which side of the body we’re throwing on

We begin by putting any information about the pattern before the slash. Then the slash shows which side of the body (left or right) the first throw peaks on. The top of the slash is where the top of the first peak will be with “/” peaking on the right side and “\” peaking on the left side. The first letter pair is what you do with the right hand and the second letter pair is what happens with the left hand. Let’s get started by looking at four patterns that are relatively easy to understand before we more on to mills mess which is a bit more complicated.

These two patterns are both just cascades. We can see that “i” makes it a regular cascade while “o” makes it a reverse cascade. None of the throws and catches are done with the arms crossed so all the throws are “U” and all the catches are “u”. The first “Uu” shows what we do with the right hand and the second “Uu” shows what we are doing with the left hand. In Pretzel Hand you always start with the right hand. The top of the slash shows which side of the body the top of the objects first arc will be on. The colon shows we change which side of the body we’re on with each throw.

Here we have two slightly more interesting patterns. The one on the left is a crossed arm cascade. All the throws are on the outside and caught on the inside so it’s an “o”. We change side with every throw so there’s a colon in the middle. But our arms are crossed with the right arm on top for all the throws and catches which makes it “Rr : Rr” (we’re looking at the juggler so their right arm is on our left). The pattern on the right is a windmill. We don’t change which side of the body we’re on so there’s no colon. The left arm is on top for all the throws from the right hand so the first throw is an “L”, where as the arms are uncrossed for the left hand throw so the second throw is a “U”. The first catch is with the right hand uncrossed so it’s an “u”. Then the next catch is with the left hand and with the left arm over the right so it’s an “l”.

The Appendix has a list of some other common patterns that might help you understand the notation if the next section is confusing. It also has a fuller list of what letters you can use before the slash.

NB Pretzel Hand uses similar letters and ideas to Mills Mess State Transition Diagram (MMSTD). I came up with it while not aware of the workings of MMSTD but in retrospect it’s very much a similar application of the same idea. I’d say its main difference is that it notates the catches as well as the throws. It also dispenses with diagrams and just focusses on the notation. In my opinion it is more intuitive and concise then MMSTD by trying to show just the most relevant info to juggle the pattern.

– What is Mills Mess?

Mills mess is a repeating pattern of six throws and catches where a three ball arc goes one direction then the other. All throws are outside throws and it involves a smooth and continuous crossing and uncrossing of the arms. Standard mills mess is written like this:

o\ Ru Ul Ll : Lu Ur Rr

I’ve colored the letters to make it easier to learn what ball the throws and catches are referring to. The first throw (R) is from the right hand with the right arm on top. The right hand then catches with the arms uncrossed (u). Then the left hand throws with the arms uncrossed (U) and catches with the left arm on top (l) etc etc. The colon shows we change which side of the body we’re on so the first three throws are thrown on one side of the body and the second three throws are on the other side.

– The Eight Base Patterns

We can use this notation to describe the eight base mills mess patterns. The first one is mills mess which we have already looked at. The second is flipped mess. Flipped patterns are where you flip the arms, so throws and catches that happen with the arms crossed over one way now happen with the arms crossed over the other way.

Then we have the time reverse (tr) of each of those two patterns giving us the first four messes. When you time reverse a mess it changes from outside throws and inside catches to inside throws and outside catches. The TR versions are specific to three objects that’s why they are “3 i” and not just “i”.

Next we have flos mess. Mills mess is made up of a crossing, uncrossing then crossing arm pattern (XUX). Flos mess switches this over so we have an uncrossing, crossing, uncrossing arm pattern (UXU). This often makes patterns feel a little easier because we cross and uncross our arms less often during the pattern. Then we have the flipped version of flos where right arm on top becomes left arm on top and vice versa.

Then finally we have the time reverse versions of both those patterns.

o\ Ru Ul Ll : Lu Ur Rr – mills mess
o\ Lu Ur Rr : Ru Ul Ll – flipped mess
3 i\ Ur Rr Ru : Ul Ll Lu – tr mills mess
3 i\ Ul Ll Lu : Ur Rr Ru – tr flipped mess
o/ Ur Ru Uu : Ul Lu Uu – flos mess
o/ Ul Lu Uu : Ur Ru Uu – flipped flos mess
3 i/ Ru Uu Ul : Lu Uu Ur – tr flos mess
3 i/ Lu Uu Ur : Ru Uu Ul – tr flipped flos mess

With mills mess variations the second half is always the mirror of the first (Ru becomes Lu and Ur becomes Ul) and the catch information is already contained in the throw because the catch is always the same as the next throw (except in hectic mills which we’ll look at later). I think it is useful to include the catch info when describing mills variations because it helps with understanding and learning these patterns.

This notation always starts with the right hand and in these mills patterns that throw is always the first of the three throw arc that is a quintessential part of mills mess. The first letter is the first throw with right hand, even if that first throw is on the left side of the body.

– Sebs Mess

Sebs mess is a modification of mills mess where you bend the pattern around you so instead of all the throws being in front of you they are on either side. For the outside cascade messes (which is mills mess, flipped mills, flos mess and flipped flos mess) you do them with forward throws (see a mills mess juggled as a sebs mess below). For the inside cascade patterns which are the time reverse versions of those patterns you do them with backward throws. The standard forward sebs is just a standard mills mess. Time reverse mills mess when done at the side of your body uses backward throws and is often called a “weave”. Time reverse flipped flos mess when juggled backward at the sides of your body is simply called “backward sebs”. The naming of this patterns is extremely confusing and hopefully a more logical naming structure will be adopted over time.

o/ Ru Ul Ll : Lu Ur Rr

– Learning Patterns with Pretzel Hand

The mills mess variations will definitely be easier to learn if you can already do a solid mills mess. Also drilling windmills on each side will help a lot (there’s more info on windmills here).

To juggle one of these patterns start with two objects in your right hand and one in your left. Here’s where to place your arms to start with based on how the pattern you are learning starts:

o\ R – Right arm over left and on the left side of your body throwing right to the middle
o\ L – Right arm under left and on the left side of your body throwing right to the middle
o/ U – Arms uncrossed and right arm on right side of your body throwing left to the middle
i\ R – Right arm over left and in the middle of your body throwing to the left side
i\ L – Right arm under left and in the middle of your body throwing to the left side
i/ U – Arms uncrossed and right arm in the middle of pattern throwing to the right side

The next letter is lowercase and the first catch. When you start a pattern you don’t need to make this catch because it should already be in your right hand (like the universe has caught it for you). But next time round you will. For now just move your hand to that position as if you were making a catch. Then keep going. Throws are uppercase, catches are lowercase. The next throw is from the left hand and then from the right. These three throws will go in the same direction. If it’s an outside pattern they are all travelling from the outside in to the middle. If it’s an inside pattern there are travelling from the middle out to the side.

If we wanted to break down the patterns to make it easier to learn we could work on just the first two throws and catches (the red and blue balls). For the standard mills mess that would be as follows. We always start with the right hand and we can see it’s an outward cascade. The first throw is an R so my right hand is going to throw from the far left of the pattern while on top of my left arm. Then the catch one and a half beats before the next throw is an l and it’s with the left hand so it’s going to be my left arm on top of my right. We can do the same thing with the blue ball and learn that pair of throws which is then mirrored on the other side this time starting with the left hand.

o\ Ru Ul Ll : Lu Ur Rr

If I wanted to learn these patterns at my sides like sebs mess then all I would do differently is throw the balls backwards if it’s an inside pattern and throw them forwards if it’s an outside pattern.

– Butterfly Messes

These patterns are where you do a mixture of inside and outside throws on the same side of the pattern. They are also sometimes called Opposite Messes or Hybrids. For example basic mills mess can be done as “3 ooi\ Ru Ul – Ll : Lu Ur – Rr”. Here I’m using the hyphen to mean we’ve changed direction of throw, but since it’s still on the same side of the colon we haven’t changed which side of the body we’re on. It’s important to remember when analysing these patterns that outside and inside throws behave differently. The focus of an outside throw is the side it starts on, whereas the focus of an inside throw is the side it lands on. Below are two of the butterfly messes using mills as the starting pattern:

These patterns look even more visually interesting when juggled at your sides like sebs mess. Below are the five butterfly patterns that derive from a standard mills mess. The rest of the patterns can be found in the pattern list in Appendix A. The other patterns such as ones based on Flos mess either don’t work because your arms would need to pass through each other, or don’t work because your arms end up not crossing at all.

3ioo\ Ru – Ul Ll : Lu – Ur Rr · Butterfly Basic Mess Opp1
3ii o\ Ru Ul – Ll : Lu Ur – Rr · Butterfly Basic Mess Opp1,2
3oi o\ Ru – Ul – Ll : Lu – Ur – Rr · Butterfly Basic Mess Opp2
3oi i\ Ru – Ul Ll : Lu – Ur Rr · Butterfly Basic Mess Opp2,3
3oo i\ Ru Ul – Ll : Lu Ur – Rr · Butterfly Basic Mess Opp3

– Hectic Messes

The eight patterns below look like hectic mills messes because twice in the sequence your arms swap directly from one arm on top to the other arm on top (Rl, Lr, rL or lR) without any uncrossed throws or catches in between. In the regular versions of these patterns there are two or four actions in a row where one arm stays on top. Here we’re jumping our arms over halfway through. If a mills or flos mess had a baby with it’s flipped sibling then their cursèd incestuous spawn would be one of these:

o\ Lu Ul Lr : Ru Ur Rl – hectic mills mess
o\ Ru Ur Rl : Lu Ul Lr – hectic flipped mess
3 i/ Ul Lr Ru : Ur Rl Lu – tr hectic mills mess
3 i/ Ur Rl Lu : Ul Lr Ru – tr hectic flipped mess

The above videos are juggled by the amazing Devin Tucker!

The hectic flos messes don’t work as smoothly as the regular mills messes but create a slightly different feel and visual:

o/ Ul Ru Uu : Ur Lu Uu – hectic flos mess
o/ Ur Lu Uu : Ul Ru Uu – hectic flipped flos mess
3i\ Lu Uu Ul : Ru Uu Ur – tr hectic flos mess
3i\ Ru Uu Ul : Lu Uu Ur – tr hectic flipped flos mess

– Siteswaps

Siteswap is a way of writing juggling patterns down that shows how many beats the objects are in the air for before you catch them. It’s really useful and well worth learning if you have some free time. You don’t have to fully understand siteswap to learn something from this section. However, you can skip it (or just look at the pretty .gifs) and the rest of the article will still mostly make sense.

If we are just describing a regular three ball mills pattern then there’s no need to mention the siteswap because it’s always “3”. However, if we’re using more balls, doing a time reverse pattern or doing a pattern that isn’t just a 3 then we can put that information at the start. For example:

4 o\ Ru Ul Ll : Lu Ur Rr
423 o\ Ru Ul Ll : Lu Ur Rr

It is interesting to note that a standard mills pattern can be done with any number of balls. So even an 8 ball mills would still use the same throwing pattern Ru Ul Ll : Lu Ur Rr and have the same three ball arc one way then the other, it would just be much higher (but a TR Mills would have a different throwing pattern). Mills messes with an even number of balls are just distortions of a fountain so the balls always stay in the same hand (see 4 ball mills below).

An object always lands a beat and a half before it’s thrown next (unless it’s a 1 which we’ll look at later). Therefore a 2 “lands” immediately because it is held or it’s a very low throw, but the hand is still moving as it’s holding the object. The 2 still counts as part of the three ball arc even if it isn’t thrown. I find it helps me to juggle the pattern if I put a “.” after the throw and catch that is just a hold so I can quickly see not to throw it. So a 423 mills looks like the pattern on the right:

So a 1 must then land -0.5 (1-1.5) beats from when it was thrown, right? Doesn’t that mean it travels back in time? Well … no, 1’s change the throwing catching pattern from a nice regular “throw, catch, throw, catch” to “throw, throw, catch, catch”. So you just have to change the catch before into a throw and what was then going to be a throw into a catch. It helps to put the immediate catch that’s done straight after the 1 in brackets, so you can see it’s caught with the other hand. Here’s 414 mills as an example, this coloring would change as the pattern continuing and the balls rotate through different positions. That’s why the animated version below and on the left uses all the same colored balls.

414 o\ R U(u)l Ll : L U(u)r Rr

An 0 in siteswap we doesn’t involve a throw or a catch but we still need to keep the hand moving so the hands are in the right place to throw and catch. Again the 0 counts as part of the three object arc. To make it clearer when a throw and catch pair don’t have an object but the hand is empty I write it with an underscore between the letters so “Ru” would become “R_u”.

423, 441 and 531 are all classic siteswaps to mills mess. You can do any of these three digit siteswaps in three different ways in a standard mills mess pattern. So you can do a 423 as a 423 mills, a 234 mills or a 342 mills. In each of these a different numbered throw is leading the three object arc. Then each of those patterns can be done eight different ways giving you a total of twenty-four mills mess 423 variations (but siteswaps will change the time reverse versions from the 3i ones that I’ve listed above). For example, above on the right is a 234 Flos Mess.

Lastly, you can attach multiplex siteswap to the start of the pattern as well. I don’t have any modifications to make it easier to juggle these patterns with pretzel hand yet, so these two patterns are only really here because I like them:

– Mills Mess Variations

There are very large number of interesting mills mess variations other than the eight base patterns. First of all let’s look at how we can extend mills mess. The pattern on the left below is a mills mess shower where we’ve added a shower to each side of the pattern. In the real world you’d juggle all the throws at the same height. The pattern on the right is a 5bt where you put an extra windmill on each side.

Next we’re going to look at half messes or Single Lubmans (so called because Ron Lubman did this version of the trick before mills mess was discovered). On the left side we have a half mess. A regular mills mess is a 3:3 pattern where the three objects arc one way then the other in a symmetrical pattern. The half mess is only a 2:2 so two balls arc one way then the other, and because of this it’s asymmetrical. But the pattern on the right shows we can make it symmetrical by doing a 2:2:2:2 version.

We can create many different combos this way. For example, if we keep our arms crossed for two more throws in the center of a regular mills mess we can do a 3:1:1:3:1:1 mess. We can also do the same with some half messes to give us 3:2:2:3:2:2 or do a combination of the two and do 3:2:2:1:1:3:2:2:1:1 or even 3:2:2:1:1:2:2:3:2:2:1:1:2:2 which I consider more of a satisfying mental exercise rather than being particularly visually pleasing. If you do a hectic throw/catch you can do a 1(hectic):1:1:1(hectic):1:1 which is an alternating cross arm cascade that feels like a very distant cousin of a mills mess.

There are many other well known mills mess variations. Some of the most famous ones are Burke’s Barrage which is a type of 423 mills mess and Rubenstein’s Revenge which is a 33522 mess (see below). My favorite variation is Mike’s Mess which is a 225 mess where you do a weave at your sides with the 2s and throw the 5 under your arm. There’s more on these patterns in Appendix B

22335 o\ Ru. Ul. Lu Ul Ll : Lu. Ur. Ru Ur Rr – Rubenstein’s Revenge
52233 i/ Ul Lu. Ur. Rr Ru : Ur Ru. Ul. Ll Lu – TR Rubenstein’s Revenge
52233 o/ Ul Lu. Ur. Ru Uu : Ur Ru. Ul. Lu Uu – Flos Rubenstein’s Revenge
33522 i\ Lu Uu Ul Lu. Ur. : Ru Uu Ur Ru. Ul. – TR Flos Rubenstein’s Revenge
35223 o\ Ru Ur Ru. Ul. Ll : Lu Ul Lu. Ur. Rr – Alt Rubenstein’s Revenge
35223 i/ Ur Rr Ru. Ul. Lu : Ul Ll Lu. Ur. Ru – TR Alt Rubenstein’s Revenge

– Appendix A: List of Patterns
– Appendix B: Building Ingenious Messes From Hulking Windmills
– Appendix C: Random Pretzel Hand Theory

Acknowledgements

Massive thanks to Eric Sipos for advising me that “flipped flos mess” is a more common name than “tr backward sebs mess”; for helping me see that I could denote switching sides of the body with a colon, allowing the description of other patterns; for helping understand “hybrids” or butterfly messes and for showing me an alternating half mess (2:2:2:2). Thanks to David Mackie and Eric Sipos for showing me that my time reverse versions didn’t just magically work when you have a different number of objects. All the animated gifs were made with Juggling Lab.

These are Juggling Lab hand path settings I used (for 3 objects):
(-25,25)(-5,12.5).(25,12.5)(-5,25).(-25,0)(5,0). – Basic Mess
(-25,0)(-5,12.5).(25,12.5)(-5,0).(-25,25)(5,25). – Flipped Mess (bps=3.5, dwell=0.75)
(5,12.5)(-25,25).(-5,0)(-25,0).(5,25)(25,12.5). – TR Basic Mess
(5,12.5)(-25,0).(-5,25)(-25,25).(5,0)(25,12.5). – Flipped TR Basic Mess (bps=3.5, dwell=0.75)
(25,12.5)(5,25).(-25,0)(5,12.5).(25,12.5)(-5,12.5). – Flos Mess
(25,12.5)(5,0).(-25,25)(5,12.5).(25,12.5)(-5,12.5). – Flipped Flos Mess (bps=3.5, dwell=0.75)
(-5,25)(25,12.5).(5,12.5)(25,12.5).(-5,12.5)(-25,0). – TR Flos Mess
(-5,0)(25,12.5).(5,12.5)(25,12.5).(-5,12.5)(-25,25). – TR Flipped Flos Mess (bps=3.5, dwell=0.75)

Appendix A: List of Patterns

Key

R – right arm on top throw
L – left arm on top throw
U – arms uncrossed throw
r – right arm on top catch
l – left arm on top catch
u – arms uncrossed catch
o – all outside throws (from outside of pattern to the center)
i – all inside throws (from center of pattern to the outside)
O – all outside to outside throws (doesn’t work with slash direction or hyphen)
I – all columns (this doesn’t work with the colon)
oii – an outside throw then two inside throws
L – the pattern starts with the left hand instead of the right. Only applies to unsymmetrical patterns.
tr – this only appears in the description and means “time reverse” i.e. if you filmed it and played it backwards
: – change which side of the body we’re throwing on
“-” – keep throwing on the same side but change the direction of the throws. Used in butterfly messes.
\ or / which side of the body the first throw peaks on. For arms crossed “\” and for arms uncrossed “/” (apart from on the basic cascades).

Basic Cascades

i\ Uu:Uu – cascade
o/ Uu:Uu – reverse cascade
O/ Uu Uu – half shower
Oii/ Uu:Uu – tennis

Rr:Rr – crossed arm cascade with right arm on top
Ll:Ll – crossed arm cascade with left arm on top
Lu Ul – clockwise windmill (under throws)
Ru Ur – clockwise flipped windmill (under catches)
Ur Ru – anticlockwise windmill (under throws)
Ul Lu – anticlockwise flipped windmil (under catches)
Ul:Ur – continuous under arm catches
Lu:Ru – continuous under arm throws

Alternating Windmills

Ru Ul Lu Ur – clockwise alternating windmill
Ur Ru Ul Lu – anticlockwise alternating windmill

Half Messes (2:2)

o\ Ru Uu : Ur Rr
o\ Lu Uu : Ul Ll
oL\ Lu Uu : Ul Ll
oL\ Ru Uu : Ur Rr
3 i\ Ru Uu : Ur Rr
3 i\ Lu Uu : Ul Ll
3 iL\ Lu Uu : Ul Ll
3 iL\ Ru Uu : Ur Rr

Alternating Half Messes (2:2:2:2)

o\ Ru Uu : Ul Ll : Lu Uu : Ur Rr
o\ Lu Uu : Ur Rr : Ru Uu : Ul Ll
oL\ Lu Uu : Ur Rr : Ru Uu : Ul Ll
oL\ Ru Uu : Ul Ll : Lu Uu : Ur Rr
3 i\ Ru Uu : Ul Ll : Lu Uu : Ur Rr
3 i\ Lu Uu : Ur Rr : Ru Uu : Ul Ll
3 iL\ Lu Uu : Ur Rr : Ru Uu : Ul Ll
3 iL\ Ru Uu : Ul Ll : Lu Uu : Ur Rr

Less Than Half A Mess (1:1:1:1)

Rr : Rl : Ll : Lr
L\ Ll : Lr : Rr : Rl

Alternating Less Than Half A Mess (1:1:1:1:1:1)

Rr : Rr : Rl : Ll : Ll : Lr

Mills Messes (3:3)

o\ Ru Ul Ll : Lu Ur Rr – mills mess
o\ Lu Ur Rr : Ru Ul Ll – flipped mess
o/ Ur Ru Uu : Ul Lu Uu – flos mess
o/ Ul Lu Uu : Ur Ru Uu – flipped flos mess

3 i/ Ur Rr Ru : Ul Ll Lu – tr mills mess
3 i/ Ul Ll Lu : Ur Rr Ru – tr flipped mess
3 i\ Ru Uu Ul : Lu Uu Ur – tr flos mess
3 i\ Lu Uu Ur : Ru Uu Ul – tr flipped flos mess

2 i\ Rr Ru Ul : Ll Lu Ur – tr mills mess
2 i\ Ll Lu Ur : Rr Ru Ul – tr flipped mess
2 i/ Uu Ul Lu : Uu Ur Ru – tr flos mess
2 i/ Uu Ur Ru : Uu Ul Lu – tr flipped flos mess

4i\ Lu Ur Rr : Ru Ul Ll – tr mills mess
4 i\ Ru Ul Ll : Lu Ur Rr – tr flipped mess
4 i/ Ul Lu Uu : Ur Ru Uu – tr flos mess
4 i/ Ur Ru Uu : Ul Lu Uu – tr flipped flos mess

Butterfly Messes

3 ioo\ Ru – Ul Ll : Lu – Ur Rr · Butterfly Basic Mess Opp1
3 iio\ Ru Ul – Ll : Lu Ur – Rr · Butterfly Basic Mess Opp1,2
3 oio\ Ru – Ul – Ll : Lu – Ur – Rr · Butterfly Basic Mess Opp2
3 oii\ Ru – Ul Ll : Lu – Ur Rr · Butterfly Basic Mess Opp2,3
3 ooi\ Ru Ul – Ll : Lu Ur – Rr · Butterfly Basic Mess Opp3

3 ioo\ Lu – Ur Rr : Ru – Ul Ll · Butterfly Flipped Mess Opp1
3 iio\ Lu Ur – Rr : Ru Ul – Ll · Butterfly Flipped Mess Opp1,2
3 oio\ Lu – Ur – Rr : Ru – Ul – Ll · Butterfly Flipped Mess Opp2
3 oii\ Lu – Ur Rr : Ru – Ul Ll · Butterfly Flipped Mess Opp2,3
3 ooi\ Lu Ur – Rr : Ru Ul – Ll · Butterfly Flipped Mess Opp3

3 oii/ Ur – Rr Ru : Ul – Ll Lu · Butterfly TR Basic Mess Opp1
3 ooi/ Ur Rr – Ru : Ul Ll – Lu · Butterfly TR Basic Mess Opp1,2
3 ioi/ Ur – Rr – Ru : Ul – Ll – Lu · Butterfly TR Basic Mess Opp2
3 ioo/ Ur – Rr Ru : Ul – Ll Lu · Butterfly TR Basic Mess Opp2,3
3 iio/ Ur Rr – Ru : Ul Ll – Lu · Butterfly TR Basic Mess Opp3

3 oii/ Ul – Ll Lu : Ur – Rr Ru · Butterfly TR Flipped Mess Opp1
3 ooi/ Ul Ll – Lu : Ur Rr – Ru · Butterfly TR Flipped Mess Opp1,2
3 ioi/ Ul – Ll – Lu : Ur – Rr – Ru · Butterfly TR Flipped Mess Opp2
3 ioo/ Ul – Ll Lu : Ur – Rr Ru · Butterfly TR Flipped Mess Opp2,3
3 iio/ Ul Ll – Lu : Ur Rr – Ru · Butterfly TR Flipped Mess Opp3

Hectic Messes

o\ Ru Ur Rl : Lu Ul Lr – hectic mills mess
o\ Lu Ul Lr : Ru Ur Rl – hectic flipped mess
o/ Ul Ru Uu : Ur Lu Uu – hectic flos mess
o/ Ur Lu Uu : Ul Ru Uu – flipped flos mess
3 i/ Ur Rl Lu : Ul Lr Ru – tr hectic mills mess
3 i/ Ul Lr Ru : Ur Rl Lu – tr hectic flipped mess
3 i\ Lu Uu Ul : Ru Uu Ur – tr hectic flos mess
3 i\ Ru Uu Ul : Lu Uu Ur – tr hectic flipped flos mess

Other Mills Mess Extensions/Variations

o\ Ru Ul Ll Ul Lu : Lu Ur Rr Ur Rr – 5bt mills with extra windmills
o\ Ru Ul Ll : Ll : Ll : Lu Ur Rr : Rr : Rr – mills with extra crossed arms
44133 o\ Ru U Uuu Ul Ll : Lu U Uuu Ur Ru – mills with shower
22335 o\ Ru. Ul. Lu Ul Ll : Lu. Ur. Ru Ur Rr – Rubenstein’s Revenge
52233 i/ Ul Lu. Ur. Rr Ru : Ur Ru. Ul. Ll Lu – TR Rubenstein’s Revenge
52233 o/ Ul Lu. Ur. Ru Uu : Ur Ru. Ul. Lu Uu – Flos Rubenstein’s Revenge
33522 i\ Lu Uu Ul Lu. Ur. : Ru Uu Ur Ru. Ul. – TR Flos Rubenstein’s Revenge
35223 o\ Ru Ur Ru. Ul. Ll : Lu Ul Lu. Ur. Rr – Alt Rubenstein’s Revenge
35223 i/ Ur Rr Ru. Ul. Lu : Ul Ll Lu. Ur. Ru – TR Alt Rubenstein’s Revenge
3 I/ Uu Uu Ur : Rr Rr Ru : Uu Uu Uu : Ll Ll Lu – 3 ball Boston mess
4 I/ Uu Uu Ul Lu: Uu Uu Ur Ru – 4 ball Boston mess

The End

– Top of This Page
– Start of Appendix A: List of Patterns
– Appendix B: Building Ingenious Messes From Hulking Windmills
– Appendix C: Random Pretzel Hand Theory