Lesson 10 for MM_STD

    ######  --+o-->  ######
    # Lr #           # Ll #
    ######  <--o+--  ######       So here is our diagram
     ^  |             ^  |        again, and we have used it
     |  +             |  +        to analyse Mills Mess and
     o  |             o  |        compute its time-reversal.
     |  v             |  v        We have also used it to
    ######  --+o-->  ######       see what the "Funky Mess"
    # Ul #           # Ur #       is, and how it's a fairly
    ######  <--o+--  ######       natural idea.
     ^  |             ^  |
     |  o             |  o
     +  |             +  |        But what about some other
     |  v             |  v        patterns?
    ######  --+o-->  ######
    # Rr #           # Rl #
    ######  <--o+--  ######

    ######  ---o-->  ######       Here's another pattern. In
    # Ul #           # Ur #       this pattern we see-saw
    ######  <---+--  ######       back and forth between the
                      ^  |        states  Ul  and  Rr, going
                      |  o        via  Ur  and  Rl  on the
                      +  |        way.  Firstly, can you
                      |  v        work out what this pattern
    ######  --+--->  ######       is?   Interpreting these
    # Rr #           # Rl #       diagrams is never easy, so
    ######  <--o---  ######       take some time to try it.
Here is the answer to the pattern above.
      + -- +      ######          Drawn at left here are
      |    |      |    #          four "skeletons" of the
      |    |      |    #          state transition diagram.
      ######      ######          The first has highlighted
      |    #      |    |          on it the pattern above -
      |    #      |    |          the three-cylinder-engine.
      ######      + -- +          This particular version
                                  has the balls being throw
                                  on the right, then middle,
      + -- +      ######          then the left, and has the
      |    |      #    |          right arm crossing on top.
      |    |      #    |          The other three give the
      ######      ######          alternatives - having the
      #    |      |    |          other arm on top, throwing
      #    |      |    |          the balls in the opposite
      ######      + -- +          direction, or both.
Transitions between these different forms of the patterns can easily be worked out by following the paths around on the full diagram, but actually juggling them may be more of a challenge !! As with all useful notations, the gain in understanding often (initially) outstrips the ability to put it into practice. However, with any luck the notation will eventually help us develop more flexibility in our juggling by giving us things to try that we'd never thought of, and the ability to understand them and communicate them to others unambiguously.

In the next lesson we'll see how to combine the diagram with SiteSwaps, and how we can sometimes avoid having to draw the full diagram.


Go to Lesson 11
Back to Lesson 9

The contents of this document are Copyright (C) Solipsys Ltd, 1996, but you may reproduce and redistribute them freely provided that you make no changes, no charges, and that this copyright notice remains attached.

Dr C.D.Wright