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File: MM_STD_05 !!! MM_STD Tutorial Part 5 Here's the main point again from MM_STD_04: * When we move from one state to another we draw an arrow and say whether the exchange was an inside exchange or an outside exchange. We then put a circle or a bar on the arrow to show whether it's an inside or an outside exchange. ********> Also recall the diagram we had for _ the right-hand throw FalseShower _ with underneath throws ... ******** images/UroRli.png ********< You are further supposed now to have drawn the diagrams for the following patterns ... 0 the left-throw FalseShower with underneath throws, 0 the left-throw FalseShower with above throws, 0 the right-throw FalseShower with above throws, 0 the cascade, 0 the reverse cascade, 0 the right-throw HalfShower. We're going to assume you've done this. If you haven't done these, take the time now. It will help quite a lot. For those of you who _have_ done the exercises, here are the answers ... ********> images/LriUlo.png ******** _ At left, _ the left-throw FalseShower _ with underarm throws, ******** _ _ _ _ At right, _ the left-throw FalseShower _ with above throws, ******** images/RriUlo.png ********< ********> images/UroLli.png ******** _ At left, _ the right-throw FalseShower _ with above throws, ******** _ _ _ _ At right, the cascade, ******** images/UriUli.png ********< ********> images/UroUlo.png ******** _ At left, _ the reverse cascade, ******** _ _ _ _ At right, _ the right-throw HalfShower. ******** images/UroUli.png ********< !! How do these fit together? Suppose you're in the middle of juggling some pattern and you find yourself in the state *Ur*. Remember, this means that your arms are uncrossed, and your right hand is about to do an exchange. What can we do now? Looking at the diagrams above there are four things we've done so far from this situation. These are ... 0 An inside throw to *Ul* 0 An outside throw to *Ul* 0 An outside throw to *Ll* 0 An outside throw to *Rl* ********> Notice that in each case the state we go to has a left throw next. Of course, this has to be the case because the hands always alternate. We can go to the state *Ul* in two different ways, one is with an inside exchange, the other is with an outside exchange. The other options are to move to an arms crossed position, either right on top or left on top, but in each case we have do do an outside throw. We can lump all this together in a single, two-dimensional diagram, as shown here. ******** images/Ur.png ********< ********> images/Most.png ******** In fact, let's put in _all_ the states, and all the arrows we've seen so far. Notice that we've been lazy and put both the *I* and the *O* on a single arrow between the *Ur* and *Ul* states, rather than having two arrows in each of the directions. It saves clutter. ********< The basic idea now is that you can wander around on this diagram, doing an exchange every time you follow an arrow. If you follow an arrow marked with a *I* then you have to do an inside exchange, and if you follow an arrow marked with a *O* you have to do an outside exchange. Of course, if the arrow has both a *I* and a *O* then you can do either type of exchange. This isn't the whole story. For one thing the diagram isn't yet complete. We also need to see how to use it to analyse patterns and invent new ones. !! Next ... MM_STD_06