###### --+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.