by Ed Carstens
I just wanted to share the process which I am currently using to come up with multi-handed patterns. I have already outlined this process in theory. Here's an example of how you can come up with a new pattern on your own. No computer program is necessary for this. The hardest calculations you make are addition and subtraction! Let's start by permuting the zero-perm. matrix for L=4,H=3: |(1,1) (1,2) (1,3) (1,4)| |(2,1) (1,2) (3,3) (2,3)| |(2,1) (2,2) (2,3) (2,4)| --> |(3,1) (2,2) (2,4) (3,4)| |(3,1) (3,2) (3,3) (3,4)| |(1,1) (3,2) (1,3) (1,4)| Now we find the relative (throw) matrix by subtracting the 0-perm.: i.e. (2,1)-(1,1)=(1,0), (1,2)-(1,2)=(0,0), etc. |(1,0) (0,0) (2,0) (1,-1)| |(1,0) (0,0) (0,1) (1,0) | |(-2,0) (0,0) (-2,0) (-2,0)| Now add 3 objects to each hand by adding (0,3) to each element: |(1,3) (0,3) (2,3) (1,2) | |(1,3) (0,3) (0,4) (1,3) | |(-2,3) (0,3) (-2,3) (-2,3)| We could stop here but the (1,2) indicates a hold which is being passed which can't happen so we have to add a (0,4) to this because L=4. Doing this adds one more object to the pattern so we may want to subtract (0,4) from another element. The only candidate for this is the (0,4) in the 3rd row,3rd col. Rob |(1,3) (0,3) (2,3) (1,6) | Rob: S3,R3,G3,S6 Steve |(1,3) (0,3) (0,0) (1,3) | or Steve: G3,S3,S0,G3 Greg |(-2,3) (0,3) (-2,3) (-2,3)| Greg: R3,G3,R3,R3 This is it! Now let me explain what these numbers mean: Each row indicates the succession of throws made by one hand. For standard passing patterns one hand can be thought of as one passer since he normally only throws with one hand at a time. Let's say Rob has the top row, Steve has the 2nd and Greg the 3rd. Rob's first instruction (1,3) tells him to pass a single to Steve. Greg's first instruction (-2,3) tells him to pass a single to Rob. Steve passes a single to Greg. (This is a triangle.) (0,3) indicates a left-right self or vamp. (0,0) indicates no catch which will occur once a pattern is underway. (Startup discussed later.) (1,6) indicates that Rob must throw a quad to Steve out of his left hand. You can convert to an easier notation for the pattern as shown on the right. Starting a pattern can be a problem. In this case we have not altered the object number since we subtracted (0,4) and added (0,4). If we had changed it, one person would have to start with an extra club or something and I have no idea how it would startup. For this particular pattern, the relative startup |(0,3)| |(0,6)| |(0,3)| will be sufficient. The quad that Steve throws himself takes the place of the quad being thrown a beat earlier from Rob.