hadamard64 T-Shirt

This design is a visual representation of a mathematical object called a Hadamard matrix. (In the mathematical form, each white square is 1, and each black square is -1.) What is special (almost magical) about this pattern is that if you compare any two rows (that is, compare squares in corresponding positions), exactly half of the squares will be the same colour and exactly half will be opposite in colour. The same can be said of any two columns. Try it! (Mathematicians would say that any two rows, or any two columns, have zero correlation.) A few other observations: The Nth row has the same sequence as the Nth column. The first (top-most) row and the first (left-most) row are all white, but all other rows and columns are exactly half white and half black. Divide the matrix in quarters (half horizontally and half vertically): Three of the quarters are identical and the fourth quarter is the negative of the others. The quarters of these quarters follow the same pattern. (etc.) Can you find and describe other patterns? The upper-left quarter is a smaller Hadamard matrix. (etc.)