Binary Color-Coded Magic Squares: A Study of Uniqueness Under Rotation/Reflection, PCA, and LDA Analysis

TL;DR

This study explores the uniqueness and patterns of binary color-coded magic squares of various orders using rotation, PCA, and LDA, revealing previously unknown mathematical insights.

Contribution

It introduces the concept of binary color-coded magic squares and applies multiple analytical methods to uncover new patterns across different types of magic squares.

Findings

Identified striking new patterns in binary color-coded magic squares.

Demonstrated the effectiveness of PCA and LDA in analyzing magic square patterns.

Revealed previously unknown structures in traditional magic squares.

Abstract

In this paper, we study the concept of "binary color-coded magic squares" by assigning two distinct colors to the even and odd numbers within a magic square. We investigate the uniqueness of patterns within these squares using three different analytical methods, including rotation/reflection, PCA, and LDA. Our investigation covers all 880 magic squares of order 4, all 48,544 associative magic squares of order 5, and all 368,640 Franklin magic squares of order 8. Our investigation reveals striking patterns that were previously unknown in traditional magic squares, shedding light on the potential for binary color-coded magic squares to contribute to the field of mathematics.