Numerical Carpets

1 June 1, 1998 Introduction It has long been known that modular arithmetic often produces interesting numerical patterns. These patterns can be made easier to comprehend and more interesting by rendering them as images with colors associated with numerical values. The example most often cited is Pascal’s Triangle, which exhibits the binomial coefficients. If you take the coefficients modulo m for various m, you get different but interesting patterns. Figures 1 through 3 show a portion of Pascal’s Triangle for m = 2, 3, and 5, using m uniformly spaced shades of gray from black (for 0) to white (for m–1).