[jugglemaster] Some implementation notes

[Chunky Kibbles]

To follow up, here's the documentation from random patterns, thanks to
Aidan Burns originally, and ripped from my own source code comments
written during actual implementation:


How to generate random siteswaps

All maths courtesy of Aidan Burns,
http://www.geocities.com/aidanjburns/


ASYNCHRONOUS PATTERNS

Seed a buffer of pattern_length with throws of height num_balls

Rule 1,  The Downright Rule: to swap any two throws in a pattern, the
throw that moves to the right decreases with each step, and the throw
that moves to the left increases with each step. A throw may not move
if it would decrease below zero.

Rule 2,  The Circular Rule: a throw may be moved from the front to the
back of a pattern.

Implemenation note: Rule 2 is implied by doing all swapping arithmetic
   modulo patt_len.


SYNCHRONOUS PATTERNS

To seed the pattern:
  1) Even numbers of balls go (n,n)<rinse, repeat>
  2) Odd numbers of balls should go ((2n-2)x,2)(2,(2n-2)x)<rinse, repeat>
  3) Unfortunately, that breaks down the notation at 18 throws, so use
    this instead: ((n+1)x, (n-1))((n-1), (n+1)x)<rinse, repeat>

Rule 3,  The Handedness Rule: when you change a throws handedness, you
change its crossedness.

Rule 4,  The Two Up, Two Down Rule: to swap any two throws in a synchronous
pattern, the throw that moves to the right decreases by two with each
bracket, and the throw that moves to the left increases by two with each
bracket. A throw may not move if it would decrease below zero.

Rule 2 is also still used, and is also still implied by the implemenation


MULTIPLEX PATTERNS

Multiplex patterns can be created by combining same-length patterns of
the either other two flavers. Example here is easier than anything else:

  5  0  4 +    ( 3 balls )
  4  2  0      ( 2 balls )
-----------
[54] 2  4      ( 5 balls )


(  4    ,   4   ) +  ( 4 balls )
(  6x   ,   6x  )    ( 6 balls )
-----------------
( [46x] , [46x] )    ( 10 balls )


Gary (-;