The Magic Square 3x3 and 9x9 matrixes X3 up to Infinity
“If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”
― Nikola Tesla
Matrix Size and Pattern Variation
A simple example, the 3x3 matrix is perhaps a very old, important, and powerful pattern hidden in plain sight. The numbers themselves reveal the relative position and sequence populating the matrix. These positions indicate the numbers within a 3x3 matrix, the position of a 3x3 matrix within a 9x9 matrix, the position of a 9x9 matrix within a 27x27 matrix continuing onward.
The 9x9 matrix . Composed of 9 - 3x3 matrix. Following the simple pattern in the 3x3 the 9x9 can be populated many different ways.
Just a random sampling of other fill patterns used in a 9x9 matrix.
The 27x27 composed of 9 - 9x9's with 9 - 3x3's each occupying 9 positions.
the pattern may be copied in a layer and the layers stacked.
The stacked layers form a 3 dimensional cube or expand into infinity .
- The core matrix is the individual matrix which can be a 3x3 , 9x9, 27x27 etc. using any of the fill patterns strictly adhering to the central pattern. Copies of the core matrix when aligned comprise a layer.
- The core matrix above is a 9x9 matrix. The 9x9 matrix is positioned in 9 layers on the Z Axis.
- A 3x3 matrix will have 3 layers on the Z-Axis, a 9x9 has 9 layers , an 81x81 has 81 layers etc.
- Each successive layer must be transposed by 1 position on the x- axis or on the y axis.
- The shifting of the layers is always performed in the same direction and each layer is shifted progressively by 1 position per layer.
- There is no limit to the maximum size of the x, y, or z axis. (The z-axis is based on the core matrix size, the core matrix size is not limited.)
- The core matrices are aligned side by side and end to end and extend indefinitely. The area or size of the core matrix can be focused anywhere, the sums in the x, y and z axis in that area of focus will be equivalent just like the Magic Square.
- If the outside edges of a column or row were brought together (producing a round tube ) the sums on the X, Y , and Z axis surrounding that connecting line would be seamless as no line would exist there at all.
- An Excel Spreadsheet with a sample 9x9x9 Magic cube is located in the Download section.
The Magic Cube 9x9x9
9x9x9 Magic Cube - 9 stacked Magic Squares
This 9x9x9 Magic Cube - 9 Magic squares of 1 to 81 stacked to produce 9 columns of equivalent sums of 369. Only 1 layer in the cube can have equivalent diagonals. On this one I arranged it to be Layer 5.
The average value of the squares surrounding the center square is the value of the center square.
An Excel spreadsheet with this Magic cube is located in the down load section.
The resulting fill in the 3x3's are incremented x9 in the 1-3, 4-6, and 7-9 positions.
Scaling the Magic Square
A pattern of Repetition of values within the scaled Magic Square
The repetition will start at a single value and increase up to a maximum value and then repeat the incremented numbers a fixed number of times until it begins descending to a single value again.
The Scaler changes the maximum value and repitions
The scaler determines the maximum minimum and incremental value within the scaled Magic Square.
Typical of Scaling the Magic Square
This is typical of how the Scaling works and its affects.
The Magic Square retains its Balance when Scaled
Scaling doesn't affect the balance of the rows and columns sums nor the average about the center.
This method is not a multiplication of a scale factor to each value.
This scaling is applied to the each cell of the final nested Magic Square. If the final Magic square is and 18x18 in a 9x9 then the scaling is applied to the values in the 18x18 as well as the 9x9.