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Alternative:
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Group Two Matrix
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Group 2
matrices can be filled in with positive, negative real or integer values
much the same as group 1.
Group 2 an also group 3 matrices have some slightly different balancing
techniques when compared to the previous group 1 methods. You will be required to
further study an understand these methods before you
are able to complete any of group 2 an group 3 matrices. Until you can
understand how to balance the group 2 matrix I will use both an
unbalance matrix to complement the finished balanced matrix. Using two
separate matrices will help you to understand the step- by-step process
of completing the balance matrix. All group 2 and group 3 matrices have
a centre cross that goes from both the upper left and upper right
diagonal. It is this centre cross that is hard fixed into the unbalanced
matrix an does not change while we complete the balanced
matrix. See shaded cells of figure 2. In
figure 2 the centre cross left diagonal is shaded yellow and the right
diagonal is shaded white. I will stay with this colour format throughout
this book. It is important that you understand the centre cross function
when doing group 2 and group 3 matrices. Unlike Group 1 you are
not required to use or understand the wrap around technique to be able
to balance the line values in the matrix. Although the wrap around technique
can be useful when animating any group matrix.
Stepping Value Explained |
If I use a stepping value of
say 3.5, then I would fill in the matrix with value of 3.5, 7, 10.5, 14 etc... The
stepping value is the incremented value from one cell to the next.
Important: You should never change the stepping value halfway through completing any matrix; the matrix may not balance if you do... You need to really know what you are doing if you decide to use randomise values in any square matrix. 4x4 Group 2 Square Matrix The first or lowest possible group 2 matrix
figure 2 |
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Balancing Any Size Group 2 Matrix Step-by-step
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16. Modified
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figure 3
| Figure 3 Step-By-Step
Explained
Figure 3 shows you a step-by-step detail description of how I fill out a group 2 matrix. The matrix is first filled in using a normal down the column counting sequence. If you where to use a difference stepping value the counting sequence would still be exactly the same. Once you have the matrix filled with the normal stepping count, you would then mark the diagonals like in figure 3-5 as not to be removed. All values not on the diagonals would then be removed as is in figure 3-6. The trick to balancing group 2 and similar group 3 types of matrices is two fold. First we count down the columns using the normal counting stepping sequence, then we start at the last removed blank cell and count back up the columns in the opposite reverse direction. For every action has an equal an opposite reaction as we are informed. We count back up the columns using the smallest to largest digits that where first removed in figure 3-5. The centre cross diagonals of group 2 matrices never change while balancing the matrix. The centre cross values can change but only when you are refining the matrix for other more advance operations. See figure 5. You should learn to balance the matrix the simple way first, before developing the principle to any advanced level. Unlike group 1 matrices, the starting cell of group 2 and group 3 matrices is from the normal upper left cell. Group 2 cells have a Ring of cells that surround the centre 4 cells similar to group 1. The difference being that you calculate the first ring from 12 cells instead of 8. The first ring of cells around the centre is 12 cells, the next ring around the first ring is then 8 cells bigger an totals with 20 cells. Example, an 8x8 matrix has 3 rings of cells around the centre. |
The first ring has 12 cells,
the second ring has 20 cells the third ring has 28 cells. Rings
propagate outward from the centre of all matrices by factors 4, 8, or
octaves if you like. Group 1 move outwards by multiples of 8 cells;
group 2 and 3 move out by multiples of 4 cells.
The centre 4 cells sum to same value as the line value of the balanced 4x4 matrix. The sum of the four corners of this 4x4 matrix also equals the Centre and the Line value. This is not the case for larger group 2 matrices. The Centre and Corner blocks will be a fractional division of the Line value for the given matrix. (See figure 7 & 8) Balanced 4x4 Group 2 Matrix
figure 4 In the balance matrix of figure 4 I have added the sum line values to show that the matrix is balanced. No matter which way you add the line values of the matrix they will always add to 34. It proves the matrix is balanced and in harmony with every other number around it. The numbers in the above matrix could represent bees around a bee hive, or petals on a flower, or the calculated individual talent of people in a sports team. What you use the matrix for is really up to you.... |
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| Modifying The Balanced
Matrix
Matrix Information:
figure 5 In the modified balanced matrix of figure 5 I have shown you how to move values in the matrix without changing the balanced structure or the line values. In the matrix the above the yellow coloured cells swap positions with the aqua coloured cells. The purpose of this exercise is to show you how you can optimise a matrix to get it to do the calculations you require. The information derived from this matrix would be difference to the original matrix of figure 4. Figure 6 shows the completed matrix of figure 5 with line values added. It is how you read or transform the valid information out of the matrix that makes matrix mathematics exciting. For most people, continually looking at the numbers of matrix would become boring very quickly. But if I where to tell those same people how to transform the numbers out of the matrix which would then enable them to build a very advanced and self running electrical energy device, then I'm sure I would have their attention. There are pages in this book dedicated to mapping real life systems through the use of matrix law. See the Reality Matrix Systems at the very begin of this book for more information. |
figure 6 There are many more marvellous patterns and functions you can implement into a matrix. In the bigger matrices you can move or swap blocks of 4,6,8 cells with other blocks of cells to derive different information from the matrix.See figure 7,8. Even though you have swapped blocks of cells the matrix will still remain balanced. It proves nature and matrix law is flexible to change with out destroying its unique and total balance to the individual domains with in nature. If this wasn't the case then nature itself would fail the first time the systems was changed or interrogated. It is the functional use of the matrix an what you map it too that makes matrices very interesting. To us human beings every thing in nature appears to be in single randomness, but nothing could be further from the truth. It is natures way to naturally balance through mathematical harmonious laws. Nature acknowledges that all things are created slightly different. Yet through the use of matrix law nature makes all things work in harmony with every other thing around it. A matrix takes the law of chaos and converts it into the law of uniformness. Individuality and uniqueness while maintaining uniformity within the whole is natures most marvellous attribute. We should never attempt force conformity onto the world unless it is from the perspective of balance though natural matrix law. Do otherwise is a recipe for disaster. The lesson of our damaged environment might be mans most painful lesson to come. Every single thing is uniquely created in itself, it is not perfect, and yet nature makes every thing work in perfect harmony with every thing else. The ability for all things to have freedom an uniqueness an yet work in perfect harmony with every other system around it, right up to the macro of the cosmos. A most marvellous state of existence to say the least. Who or what mapped this mathematical precision into the laws of nature? Natural Matrix Law is mathematical in origin. In any persons language mathematics is a conscious thought process brought about by conscious will or intervention. Am I trying to put God back into the scientific equation? Natural Matrix law could not have been left to pure change, as stated in the theory of evolution by ¹Charles Darwin. Knowing now that nature has precise mathematical laws, could the universe have been created instead of just evolved or expressed through the big bang theories ? As you progress through this book you may start to ask yourself this very same question. |
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8x8 Group 2 MatrixMatrix Information:
figure 7
figure 8 |
The matrix of figure 7 and 8 are a good demonstration of why group 2 matrices are evenly divisible by four. The 8x8 matrix uses 4 smaller 4x4 matrices to complete the larger 8x8. The principle to completing an 8x8 matrix is identical to the smaller 4x4 matrix except that we are using the reverse counting technique over the whole matrix instead of the single individual 4x4 blocks. Remember all the diagonal cell values remain in the same position as the unbalanced matrix. See figure 7. In the matrix of figures 7,8 I have coloured all the left diagonals yellow and the right diagonals white. This will help you identify the diagonals associated with each 4x4 block in the larger matrix. You can further modify or transpose the individual diagonal cells of 4x4 matrices inside this larger 8x8 much the same as we had done in the modified matrix of figure 5. If you decide to swap the individual cell diagonal values you will be required to swap all diagonal values of every 4x4 block inside the larger matrix, otherwise the matrix will no longer balance. You can also swap entire 4x4 blocks of the matrix with a 4x4 block diagonally opposite it. You may now begin to understand the matrix within a matrix principle I had explained earlier in this book. How matrices are made up of smaller matrices. There are many numerous an marvellous function to all matrices. I have only briefed on the basics of these matrix principles. See the Reality Matrix System pages for more detail information. ¹ Darwin's theory of evolution. |
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