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Manuscripts about chaos magic are a valuable and intriguing resource for those interested in the study and practice of this mystical art. Chaos magic is a modern occult practice that emerged in the late 20th century. It is a relatively new form of magic that draws from various traditions and beliefs, allowing practitioners to create their own reality and manipulate the world around them. Manuscripts about chaos magic often delve into the theoretical foundations and principles of this magical system. They explore concepts such as sigil magic, the use of symbols to manifest desires, and the importance of belief and intention in the practice of magic. These manuscripts provide a comprehensive understanding of chaos magic and its potential applications.

I found, that for a m x n matrix where the m or n is a power of 2, you can calculate the sum as sum_range(0, m-1) * n, where sum range literally just adds every number between the first and second input. Things get interesting when neither m nor n is a power of 2. You can split the m x n rectangle into a rectangle composed of sub m x n rectangles that are powers of two, like this: (15 x 15)

0, 1, 2, 3, 4, 5, 6, 7 8, 9, 10, 11 12, 13 14 1, 0, 3, 2, 5, 4, 7, 6 9, 8, 11, 10 13, 12 15 2, 3, 0, 1, 6, 7, 4, 5 10, 11, 8, 9 14, 15 12 3, 2, 1, 0, 7, 6, 5, 4 11, 10, 9, 8 15, 14 13 4, 5, 6, 7, 0, 1, 2, 3 12, 13, 14, 15 8, 9 10 5, 4, 7, 6, 1, 0, 3, 2 13, 12, 15, 14 9, 8 11 6, 7, 4, 5, 2, 3, 0, 1 14, 15, 12, 13 10, 11 8 7, 6, 5, 4, 3, 2, 1, 0 15, 14, 13, 12 11, 10 9 ---------------------------------------------------- 8, 9, 10, 11, 12, 13, 14, 15 0, 1, 2, 3 4, 5 6 9, 8, 11, 10, 13, 12, 15, 14 1, 0, 3, 2 5, 4 7 10, 11, 8, 9, 14, 15, 12, 13 2, 3, 0, 1 6, 7 4 11, 10, 9, 8, 15, 14, 13, 12 3, 2, 1, 0 7, 6 5 ---------------------------------------------------- 12, 13, 14, 15, 8, 9, 10, 11 4, 5, 6, 7 0, 1 2 13, 12, 15, 14, 9, 8, 11, 10 5, 4, 7, 6 1, 0 3 ---------------------------------------------------- 14, 15, 12, 13, 10, 11, 8, 9 6, 7, 4, 5 2, 3 0 ----------------------------------------------------. If the row exceeds or is not in the matrix, change the column to the left column, place the number at the last row of the matrix, and try again for the top left corner.

These manuscripts provide a comprehensive understanding of chaos magic and its potential applications. One of the key ideas in chaos magic is the concept of belief shifting. The belief that holds the greatest power and influence is the one that is most strongly held.

Magic Square

A is a grid of numbers arranged so that the sum of each row, each column and its diagonals are all equal to the same value, called the magic sum (or magic constant).

are popular for their simplicity and mathematical properties.

How to create a magic square?

A arranges numbers so that their placement follows construction rules that ensure that the sums of rows, columns, and diagonals equal the magic sum.

Construction methods vary depending on the order of the square (number of rows/columns).

How to create a magic square of odd order?

The creation of of size (3,5,7 etc.) is possible by several methods, the simplest is the so-called Loubère method (staircase method):

Place 1 in the center of the first line, then the following numbers in the box located diagonally at the top left. If the box is outside the square, imagine that the square wraps around itself and continue on the other end (as if the left column were to the right of the right column, and the bottom line, at the above the top line). If the target square is occupied, then continue directly below the last filled square.

Example: Staircase method generating a of order 3:

Example: Staircase method generating a of order 5 :

How to create a magic square of even order?

Creating of even order (4,6,8, etc.) is more complicated and the methods are not universal.

Symmetry method for squares of size 4:

— Place the numbers naturally from 1 at the top left to 16 at the bottom right.

— Replace the numbers on the sides (2, 3, 5 and 9) by their central symmetry (relative to the center of the square).

Other methods generally rely on creating odd subsquares.

How to solve a magic square?

The magic way to solve is to set the equations that govern each row and column, with unknowns. The constraints being that the unknowns are all different positive integers (distinct including numbers already placed).

Example: The of magic value $ X $

The equations obtained sometimes have several solutions.

What are the minimal possible sums (magic values)?

The constant values $ M $ of the sums of the have a minimum value (for non-zero integer positive values).

For a size 3x3, the minimum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it is 111, then 175, 260, …

Any lower sum will force the use of either negative numbers or fractions (not whole numbers) to solve the .

What are the maximal possible sums (magic values)?

The values can be as large as you want, so the maximum magic sum/value is infinity.

What is a panmagic square?

A panmagic square, also called a pandiagonal square, is a special type of . Unlike traditional , where only rows, columns, and major diagonals have equal sums, a panmagic square has an additional property: the sums of the numbers along all its diagonals (including minor diagonals) are equal. also equal to the magic sum.

Is there a Magic Square in 3D (Magic Cube)?

Yes, there are magic cubes, their magic value is $$ M = n(n^3+1)/2 $$ (which may or may not have magic diagonals)

What is the Franklin Square?

Franklin's square, published in 1769 by Benjamin Franklin, is a semi-panmagic square with a magic constant of 260.

Example:

What is the Lo-Shu Magic Square?

This is a 3x3 used in Feng Shui which is represented as well

What is the KaldorMagic Square?

Kaldor's is a square used in economics, which has nothing to do with digits or numbers of mathematics but rather with concepts from economic policy.

Therefore, chaos magicians aim to adopt beliefs that serve them best and empower them to create the reality they desire. These manuscripts provide guidance on how to shift and adopt beliefs effectively. Chaos magic manuscripts also discuss practical techniques for performing rituals and spellcasting. They often include instructions for creating and charging sigils, a popular form of magic in chaos magic. Sigils are symbols that represent a desired outcome, and their creation and activation are key to manifesting desires. Furthermore, chaos magic manuscripts often explore the philosophy and ethics surrounding this practice. They emphasize personal responsibility and encourage practitioners to live a life aligned with their true will. The idea of personal freedom, the ability to choose one's own beliefs and practices, is at the core of chaos magic. In conclusion, manuscripts about chaos magic are a valuable resource for those interested in exploring this mystical practice. They provide a comprehensive understanding of the theoretical foundations and practical applications of chaos magic, offering guidance on belief shifting, spellcasting techniques, and ethical considerations. These manuscripts are essential for aspiring chaos magicians looking to explore their own potential and create their desired reality..

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