  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.
