List of siteswaps

Siteswap beats shown as relative height[1][2]
<3p3|3p4|3p5|3p1|3p2><3|3|3|3|3><3|3|3|3|3><3|3|3|3|3>

Below is a list of siteswaps or juggling patterns by siteswap.

Toss juggling requires more balls than hands.[3] Thus tricks such as the one ball cascade toss back and forth, 300,[4] for example, may not be considered valid patterns. Throws back and forth shower style, odd numbers, are the most common one prop practice. Invalid or practice patterns and tricks are marked with an X.

The numbers are as follows:[5]

Symbols:

  • Number: Relative height of a toss. 1, 2, 3...
  • Brackets []: Multiplex. [333]33.
  • Chevrons and vertical bar <|>: Simultaneous and passing patterns.
    • P: Pass. <333P|333P>
    • Fraction: Pass 1/y beats later. <4.5 3 3 | 3 4 3.5>
  • Parentheses (): Synchronous pattern.
    • *: Synchronous pattern that switches sides. (4,2x)(2x,4) = (4,2x)*
    • x: Toss to the other hand during a synchronous pattern.

Asynchronous

A pattern is symmetrical (S) if both hands play the same role and asymmetrical (A) if not. All asynchronous patterns whose period is odd are symmetrical, and all asynchronous patterns whose period is even are asymmetrical.

Juggling patterns by siteswap
Siteswap Name Props Period Symmetry
(S/A)
0
X 		Empty hand 0 1 S
1
X 		Direct toss to other hand 1 1 S
2
X 		Holding a prop in each hand 2 1 S
3
 Cascade,[4][6][7][8][9][10][11]
reverse cascade,[12] etc.[13][14][15] 		3 1 S
4
 Fountain, etc.[4][10][11][16][17] 4 1 S
5
 Cascade,[4][18][19]
reverse cascade,[20] etc.[21] 		5 1 S
6
 Fountain[22][23] 6 1 S
7
 Cascade 7 1 S
8
 Fountain 8 1 S
9
 Cascade 9 1 S
20
X 		Hold a prop in 1 hand,
0 in the other[6] 		2 2 A
31
X 		Two prop shower[4][6][24] 2 2 A
40
 2 in 1 (single handed column/fountain)[4][24][25]
only valid two prop juggling pattern 		2 2 A
42
 2 in 1, hold 1 in the other[6][7][9][25] 3 2 A
51
 Shower[4][6][9][24][26][27][28] 3 2 A
53
 Half shower[4][6][7][29][30][31] 4 2 A
60
 Three in one[24][32][33] 3 2 A
62
 3 in 1, hold in the other 4 2 A
64
 3 in 1, 2 in the other[4][7][34] 5 2 A
71
 Shower[4][6][30][35] 4 2 A
73
 Half shower (see synchronous)[7] 5 2 A
75
 Half-shower[4][34] 6 2 A
80
 Four in one[30] 4 2 A
82
 Four in one, hold in the other 5 2 A
84
 Four in one, two in the other[34] 6 2 A
86
 Four in one, three in the other 7 2 A
91
 Shower[4][34][36] 5 2 A
93
 Half-shower[34] 6 2 A
95
 Half-shower 7 2 A
97
 Half-shower 8 2 A
312
X 		Shower alternating direction[4][24] 2 3 S
330
X 		Cascade with a "hole"[7][37] 2 3 S
423
 Burke's barrage,
etc.[4][6][7][10][24][38][39][40] 		3 3 S
432
 Weave[41] 3 3 S
441
 Half box[4][6][7][9][11][24][29][42][38][43][44]
and reverse,[45] Mills Mess[46] 		3 3 S
453
 453[6] 4 3
501
 High shower variant[4][6][7][24] 2 3 S
504
 504,[38][47] 450[6][11][48] 3 3 S
522
 522[4][49] 3 3 S
531
 531[4][6][7][9][10][24][50] and
531 Mills Mess[51][52] 		3 3 S
533
 533[4] 3 3 S
534
 534[4][7][10][38][53][54] 4 3 S
552
 4 out of 5[4][7][55][56] 4 3 A
561
 561[6][7][38] 4 3 S
612
 See-saw[4][24][57] 3 3 S
615
 615[4][58] 61616,[6] 4 3 S
633
 633[4][6][7][10][38][59] 4 3 S
642
 642[6][38] 4 3 S
645
 645[4][6] 5 3 S
663
 663[38] 5 3 S
714
 714[4][6] 4 3 S
723
 723[6] 4 3 S
726
 726[4] 5 3 S
741
 741[6] 4 3 S
744
 744[4][38] 5 3 S
756
 756[4] 6 3 S
771
 771[4][6][38] 5 3 S
753
 753[38] 5 3 S
801
 801[4][24] 3 3 S
810
 810[38] 3 3 S
831
 831[38] 4 3 S
867
 867[4] 7 3 S
915
 915[4] 5 3 S
945
 459[38] 6 3 S
978
 978[4] 8 3 S
3342
 3342[6] 3 4 A
4413
 4413[6][7] 3 4 A
4440
 Gap/3 out of 4 (fountain)[6][60][61] 3 4 A
5223
 Slow half-shower[62] 3 4 A
5241
 5241[6] 4 4 A
5313
 Asymmetric version of 531)[6][7] 3 4 A
5524
 5524[7] 4 4 A
5551
 5551[4][6][38][63][64] 4 4 A
6312
 6312[65] 3 4 A
6424
 6424[6] 4 4 A
7131
 High-Low Shower[66] 3 4 A
7333
 7333[4] 4 4 A
7531
 7531[6][38] 4 4 A
7562
 7562[6][38] 5 4 A
7571
 7571[6] 5 4 A
8040
 High-low three in one[4][57] 3 4 A
9955
 9559[38] 7 4 A
40141
X 		40141[38] 2 5 S
42333
 Marden's Marvel and Relf's Factory[67] 3 5 S
42423
 Orinoco Flow[68] (423 with an extra 4) 3 5 S
44133
 Frostbite and Mills Mess Shower[69] 3 5 S
45141
 45141[48][38] 3 5 S
50505
 Chase,[70] snake,[6][71][72] etc.[4][7] 3 5 S
51414
 51414[73] 3 5 S
52233
 Rubenstein's Revenge
and Romeo's Revenge[74] 		3 5 S
52512
 Boston shuffle,[75] "baby",[6] etc.[7][76] 3 5 S
52512*
 Burke's Slam,[77] (5251221525) 3 5 S
53133
 Shuffler's mess[78] 3 5 S
53444
 Tennis[71][79] 4 5 S
55014
 55014[80] 3 5 S
55244
 55244[7] 4 5 S
55500
 "Flash" (3 out of 5)[6][7][9][71][4][57] 3 5 S
55514
 55514[6][38][81] 4 5 S
55550
 Gap/four out of five[6][7][82][83] 4 5 S
56414
 56414[6] 4 5 S
66161
 66161[4] 4 5 S
66661
 66661[4][6] 5 5 S
67561
 67561[6] 5 5 S
68141
 68141[4] 4 5 S
75751
 75751[6] 5 5 S
77731
 77731[4] 5 5 S
81411
 Super box[4] 3 5 S
88333
 88333[4] 5 5 S
94444
 94444[4] 5 5 S
95353
 95353[4] 5 5 S
97333
 97333[4] 5 5 S
97441
 97441[4] 5 5 S
97522
 97522[4] 5 5 S
517131
 One up one down[4][84] 3 6 A
615150
 Shower with a "leak"[7] 3 6 A
661515
 661515[6] 4 6 A
719131
 One high one low[4] 4 6 A
777171
 777171[6] 5 6 A
5224233
 Relf's Rubensteins[85] 3 7 S
7161616
 7161616[6] 4 7 A
7272712
 7272712[6] 4 7 A
33333342
 Icelandic Shuffle[86] 3 8 A
123456789
 123456789[4][87] 5 9 S
8483848034
 8483848034[88] 5 10 A
53145305520
 53145305520 3 11 S

Synchronous

(6x,4)(4,2x)(4,6x)(2x,4)
Juggling patterns by siteswap
Siteswap Name Props Period Symmetry
(S/A)
(2x,4x)
 Half-shower[89] 3 1 S
(4,2)
 Fake Columns, yo-yo etc.[90]
(identical to 42[7]) 		3 1 S
(4,2x)(2x,4)
 Box[6][7][9][91][92] 3 2 A
(4,4)
 Columns, etc.[93][94] 4 1 S
(4,4)(4,0)
 Columns/One Up Two Up[7][9][95][96] 3 2 A
(4,4)(4x,0)
 Alternating columns[97] 3 2 A
(4,6x)(2x,4)
 (4,6x)(2x,4)[98] 4 2 A
(4x,2x)
 Shower[6][88][99] 3 1 S
(4x,2x)(4,2x)(2x,4x)(2x,4)
 Double box[6] 3 P A
(4x,4x)
 Crossing columns[9][100] 4 1 S
(4x,6)(6,4x)
 Box[4][98] 5 2 A
(6,2x)(6,2x)
 Box[101] 4 2 A
(6,2x)(6,2x)(2x,6)(2x,6)
 (6,2x)(6,2x)(2x,6)(2x,6)[6] 4 4 A
(6,4)
 3 in 1, 2 in the other 5 1 S
(6,4x)(4x,2)
 (6,4x)(4x,2)[98] 4 2 A
(6,6)(6,2)
 3 in 1, 2 in the other[6] 5 2 A
(6,6)(6,6)(6,0)
 3 in 1, 2 in the other[7] 5 3 S
(6x,2)(6,2x)(2,6x)(2x,6)
 (6x,2)(6,2x)(2,6x)(2x,6)[6] 4 4 A
(6x,2x)
 Shower[9][102] 4 1 S
(6x,2x)(2x,6x)
 Box shower/shower box[6][103] 4 2 A
(6x,4)(4,2x)(4,4)(4,6x)(2x,4)(4,4)
 Tennis[104] 4 6 A
(6x,4)(4,2x)(4,6x)(2x,4)
 Synchronous 534[105] 4 4 A
(6x,4)(4,6x)
 (6x,4)(4,6x)[15] 5 2 A
(6x,4x)
 Half shower[7] 5 1 S
(6x,6x)(2x,2x)
 (6x,6x)(2x,2x)[9] 4 2 A
(8,2x)(4,2x)(2x,8)(2x,4)
 Dan Bennett's box[6] 4 4 A

Passing

Juggling patterns by siteswap
Siteswap Name Props Period Symmetry
(S/A) 		Timing
(S/A)
<3p|3p>
 One-count[9] 6 1 S A
<3p3|3p3>
or <33p|33p>
 Two-count[9] 6 2 A A
<3p33|3p33>
 Three-count 6 3 S A
<3p333|3p333>
 Four-count 6 4 A A
<5p333><335p3>
 Simplest 4 count 7 prop[106] 7 4 A A

Ladder diagrams

Half-box: 441 
53145305520 
Box: (4,2x)(2x,4) 
Burke's barrage: 423 
Cascade: 3 
Columns: (4,4)(4,0) 
Columns, alternating: (4,4)(4x,0) 
Rubenstein's revenge: 52233 
Shower (asynchronous): 51 
Shower (synchronous): (4x,2x) 
Fountain (asynchronous): 4 
Fountain (synchronous): (4)(4) 

References

  1. ↑ After Donahue, Bill (2004). "The Mathematics of...Juggling", DiscoverMagazine.com.
  2. ↑ Tiemann, Bruce and Magnusson, Bengt (1991). "A Notation for Juggling Tricks, A LOT of Juggling Tricks", Juggle.org. Accessed July 8, 2014.
  3. ↑ For example, "1. What is juggling?", IJDb at the Wayback Machine (archived December 1, 2008). Cited in Rosenberger, Phillip (2011). Juggling Basics, Why and How To. ISBN 9780983339700.
  4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 Darley, Vincent (1996). "Site Swaps: Examples", Juggling.org. Accessed: October 24, 2016.
  5. ↑ "Juggling by numbers: How notation revealed new tricks", BBC.com (BBC article with explanatory video)
  6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 Knutson, Allen (1993). "Siteswap FAQ", Juggling.org, one page. Accessed: October 30, 2016.
  7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Phillips, Greg (2001). "Understanding Siteswap". Accessed 11 3 2016.
  8. ↑ "Cascade", LibraryofJuggling.com. Accessed: October 24, 2016.
  9. 1 2 3 4 5 6 7 8 9 10 11 12 13 "Siteswap notation", JugglingLab. Accessed: October 24, 2016.
  10. 1 2 3 4 5 6 Burns, Aiden. "Notations: Ladder Diagrams", p.11. Aidan's Juggling Page. Accessed: 11 10 2016.
  11. 1 2 3 4 Buhler, Joe; Graham, Ron (2004). "Juggling Patterns, Passing, and Posets". In Hayes, David F.; Shubin, Tatiana. Mathematical Adventures for Students and Amateurs. The Mathematical Association of America. p. 100-1. ISBN 0-88385-548-8. Retrieved February 17, 2011.
  12. ↑ "Reverse Cascade", LibraryofJuggling.com. Accessed: October 24, 2016.
  13. ↑ "Statue of Liberty", Tunbridge Wells Juggling Club.
  14. ↑ "Mill's mess", "Reverse Mills Mess", "Flipped Mess", "Boston Mess", "Half-Shower", "Cherry Picker", "Chops", "Reverse Chops", "Statue of Liberty", "Half-Mess", "Mike's Mess", "Crossed Arm Cascade", "Crossed-Arm Reverse Cascade", "Inverted Shower", "Backcrosses", "Flo's Mess", "Windmill", "Chop Shower", "Frantic Cascade", "Kraken", "Relf's Revenge 6", and "Juggler's Tennis"; LibraryofJuggling.com. Accessed: October 24, 2016.
  15. 1 2 Beever (2001), p.6.
  16. ↑ "Fountain", "Four Ball Mills Mess", and "Four Ball Half-Mess"; LibraryofJuggling.com. Accessed October 24, 2016.
  17. ↑ "Four Ball Fountain", Aidan's Juggling Page. Accessed: November 3, 2016.
  18. ↑ "Five Ball Cascade", LibraryofJuggling.com. Accessed: October 24, 2016.
  19. ↑ "The Five Ball Cascade", Aidan's Juggling Page. Accessed: November 3, 2016.
  20. ↑ "Reverse Five Ball Cascade", LibraryofJuggling.com. Accessed: October 24, 2016.
  21. ↑ "Shuffle" and "Low Shuffle", LibraryofJuggling.com. Accessed: October 24, 2016.
  22. ↑ "Six Ball Fountain", LibraryofJuggling.com. Accessed: October 24, 2016.
  23. ↑ "The Six Ball Fountain", Aidan's Juggling Page. Accessed: November 3, 2016.
  24. 1 2 3 4 5 6 7 8 9 10 11 Beever, Ben (2001). "Siteswap Ben's Guide to Juggling Patterns", p.60, JugglingEdge.com. BenBeever.com at the Wayback Machine (archived August 10, 2015), accessed: 11 3 2016.
  25. 1 2 "Two In One Hand", Adian's Juggling Page. Accessed November 3, 2016.
  26. ↑ "Shower", LibraryofJuggling. Accessed: October 24, 2016.
  27. ↑ Beever (2001), p.8.
  28. ↑ "The Three Ball Shower", Aidan's Juggling Page. Accessed: 11 10 2016.
  29. 1 2 Beever (2001), p.13.
  30. 1 2 3 Beever (2001), p.61.
  31. ↑ "Four Ball Half-Shower", Aidan's Juggling Page. Accessed: November 3, 2016.
  32. ↑ "Three in One", LibraryofJuggling.com. Accessed: October 24, 2016.
  33. ↑ Burns, Aidan. "Three In One Hand", Aidan's Juggling Page. Accessed: November 3, 2016.
  34. 1 2 3 4 5 Beever (2001), p.62.
  35. ↑ "Four Ball Shower", LibraryofJuggling.com. Accessed October 24, 2016.
  36. ↑ "Five Ball Shower", LibraryofJuggling. Accessed: October 24, 2016.
  37. ↑ "Three Ball Gap", Adian's Juggling Page. Accessed November 3, 2016.
  38. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Borwein, Jonathan M.; ed. (1997). Buhler, Eisenbud, Graham, Wright. "Juggling Drops and Descents", Organic Mathematics: Proceedings of the Organic Mathematics Workshop, December 12–14, 1995, Simon Fraser University, Burnaby, British Columbia, p.141-2. American Mathematical Soc. ISBN 9780821806685.
  39. ↑ "423", "Follow", "Burke's Barrage", "Relf's Revenge", "Fake Mess", "Takeouts", and "The W"; LibraryofJuggling.com. Accessed: October 24, 2016.
  40. ↑ "Four Two Three", Aidan's Juggling Page. Accessed: 11 10 2016.
  41. ↑ "Weave", LibraryofJuggling.com. Accessed: October 24, 2016.
  42. ↑ "Half-Box", LibraryofJuggling.com. "There have been attempts at giving it a name (some have tried to call it Parallel Schizophrenic), but none of them have stuck." Accessed: October 24, 2016.
  43. ↑ Burns, Aidan. "The Three Ball Cascade", Aidan's Juggling Page. Accessed: November 3, 2016.
  44. ↑ "Four Four One", Aidan's Juggling Page. Accessed: 11 10 2016.
  45. ↑ "Reverse Half-Box", LibraryofJuggling. Accessed: October 24, 2016.
  46. ↑ "441 Mills Mess", LibraryofJuggling.com. Accessed: October 24, 2016.
  47. ↑ "Five O Four", Aidan's Juggling Page. Accessed: 11 10 2016.
  48. 1 2 Wright, Colin and Lipson, Andrew (1996). "SiteSwaps, How To Write Down A Juggling Pattern: A Guide For The Perplexed", Juggling.org. Accessed: October 24, 2016.
  49. ↑ Beever (2001), p.15.
  50. ↑ "531", LibraryofJuggling.com. Accessed: October 24, 2016.
  51. ↑ "531 Mills Mess", LibraryofJuggling.com. Accessed: October 24, 2016.
  52. ↑ "Five Three One", Aidan's Juggling Page. Accessed: 11 10 2016.
  53. ↑ "534" and "534 Mills Mess", LibraryofJuggling.com. Accessed October 24, 2016.
  54. ↑ "Five Three Four", Aidan's Juggling Page. Accessed: November 3, 2016.
  55. ↑ "552", LibraryofJuggling.com. Accessed October 24, 2016.
  56. ↑ "Five Five Two", Aidan's Juggling Page. Accessed: November 3, 2016.
  57. 1 2 3 Morgan, Alan (1996). "Siteswaps for the Masses", Juggling.org. Accessed: October 24, 2016.
  58. ↑ "Six One Five", Aidan's Juggling Page. Accessed: November 3, 2016.
  59. ↑ "Six Three Three", Aidan's Juggling Page. Accessed: November 3, 2016.
  60. ↑ "Four Ball Gap", LibraryofJuggling.com. Accessed: October 24, 2016.
  61. ↑ "Four Ball Gap", Aidan's Juggling Page. Accessed: November 3, 2016.
  62. ↑ "The Slow Half-Shower", Aidan's Juggling Page. Accessed: 11 10 2016.
  63. ↑ "5551", LibraryofJuggling.com. Accessed October 24, 2016.
  64. ↑ "Five Five Five One", Aidan's Juggling Page. Accessed: November 3, 2016.
  65. ↑ Beever (2001), p.37.
  66. ↑ "High-Low Shower", LibraryofJuggling.com. Accessed: October 24, 2016.
  67. ↑ "Marden's Marvel", LibraryofJuggling.com and "Relf's Factory", LibraryofJuggling.com. Accessed: October 24, 2016.
  68. ↑ "Orinoco Flow", Libraryofjuggling.com. Accessed: October 24, 2016.
  69. ↑ "Frostbite" and "MillsMessShower", Libraryofjuggling.com. Accessed: October 24, 2016.
  70. ↑ Burns, Aidan. "The Chase", Aidan's Juggling Page. Siteswap: 55050. Accessed: November 3, 2016.
  71. 1 2 3 Lee, Xah (2005). "Siteswap", XahArts.org. Accessed: November 8 2016.
  72. ↑ "Snake", LibraryofJuggling.com. Accessed: October 24, 2016.
  73. ↑ "Five One Four One Four", Aidan's Juggling Page. Accessed: 11 10 2016.
  74. ↑ "Rubenstein's Revenge" and "Romeo's Revenge", LibraryofJuggling. Accessed: October 24, 2016.
  75. ↑ "Boston Shuffle", Libraryofjuggling.com. Accessed: October 24, 2016.
  76. ↑ "Peter's Shuffle", Libraryofjuggling.com. Accessed: October 24, 2016.
  77. ↑ "Burke's Slam"", LibraryofJuggling.com. Accessed: October 24, 2016.
  78. ↑ "Shuffler's Mess", Libraryofjuggling.com. Accessed: October 24, 2016.
  79. ↑ "Four Ball Tennis", Aidan's Juggling Page. Accessed: November 3, 2016.
  80. ↑ "Five Five 0 One Four", Aidan's Juggling Page. Accessed: November 3, 2016.
  81. ↑ "Five Five Five One Four", Aidan's Juggling Page. Accessed: November 3, 2016.
  82. ↑ "55550", LibraryofJuggling.com. Accessed October 24, 2016.
  83. ↑ "Five ball Gap ", Aidan's Juggling Page. Accessed: November 3, 2016.
  84. ↑ "Shower Cascade", LibraryofJuggling.com. Accessed: October 24, 2016.
  85. ↑ "Relf's Rubensteins", Libraryofjuggling.com. Accessed: October 24, 2016.
  86. ↑ "Icelandic Shuffle", LibraryofJuggling.com. Accessed: October 24, 2016.
  87. ↑ Diaconis, Persi and Graham, Ron (2011). Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks, p.144. Princeton University. ISBN 9781400839384. "Mathematically interesting siteswap patterns, such as 123456789."
  88. 1 2 Beever (2001), p.9.
  89. ↑ "The Three Ball Half-Shower (4x,2x)", Aidan's Juggling Page. Accessed: November 3, 2016.
  90. ↑ "Fake Columns", "Yo-Yo", and "Oy-Oy"; LibraryofJuggling.com. Accessed: October 24, 2016.
  91. ↑ "Box", LibraryofJuggling.com. Accessed: October 24, 2016.
  92. ↑ "The Box (4,2x)(2x,4)", Aidan's Juggling Page. Accessed: November 3, 2016.
  93. ↑ "Four Ball Columns", "Pistons", "Synchronous Pistons", and "Synchronous Fountain"; LibraryofJuggling.com. Accessed October 24, 2016.
  94. ↑ "Synchronous Four Ball Fountain", Aidan's Juggling Page. Accessed: 11 10 2016.
  95. ↑ "Columns", LibraryofJuggling. Accessed: October 24, 2016.
  96. ↑ "One Up Two Up", Aidan's Juggling Page. Accessed: November 3, 2016.
  97. ↑ "Infinity" and "Reverse Infinity"; LibraryofJuggling.com. Accessed: October 24, 2016.
  98. 1 2 3 Burns, p.19.
  99. ↑ Burns, p.18.
  100. ↑ "Synchronous Four Ball Crossing Pattern", Aidan's Juggling Page. Accessed: 11 10 2016.
  101. ↑ "Four Ball Box", LibraryofJuggling.com. Accessed October 24, 2016.
  102. ↑ "Synchronous Half Shower (6x,2x)", Aidan's Juggling Page. Accessed: November 3, 2016.
  103. ↑ "Six Two (6x,2x)(2x,6x)", Aidan's Juggling Page. Accessed: November 3, 2016.
  104. ↑ "Synchronous Four Ball Tennis", Aidan's Juggling Page. Accessed: November 3, 2016.
  105. ↑ "'Synchronous 534' (6x,4)(4,2x)(4,6x)(2x,4)", Aidan's Juggling Page. Accessed: November 3, 2016.
  106. ↑ Beever (2001), p.43.
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