### Patterns in Pascal's Triangle Modulo 2, 3, 4 and 6

Designer and Artist: Jean MacGregor Horn

Material and Method: Counted Cross-stitch on #14 Aida Cloth

Year of Creation: Stitched in 2008--9

The original charting for this was probably done in the 1970s when I
was in grad school and fooling around on graph paper with colored markers. At least that's when the idea of looking at Pascal's Triangle modulo various integers originated for me. What became interesting, but not surprising, was that the remainders modulo a prime followed a certain type of pattern (shown here with modulo 2 and 3--diagonally across from one another).
More interesting, however, is what happens when the composite numbers are used. Here I used modulo 4 (placed next to modulo 2) so you can clearly see how the modulo 2 pattern is repeated as the modulo 4 pattern is established.
I used modulo 6 as the fourth segment of this since I had already done the modulo 2 and modulo 3 designs and placed it between them. It is interesting to see how both the patterns for modulo 2 and modulo 3 appear in the modulo 6 design. They overlap briefly and then separate but both patterns are definitely there.