Regruntled.com

I took a solved sudoku, replaced the numbers with colors, and generated this image. I added a black background to separate the colors and make it easier to see the 3-by-3 blocks.

Sudokus are tileable. If you take the three blocks from the left of a sudoku and move them around to the right, you still have a sudoku. Similarly, you can move blocks from the top to the bottom. Consequently, if you repeat the pattern, you can pick out any 3-by-3 block and the 8 surrounding blocks, and you have a sudoku.

Unlike the plaids, this pattern is not weavable from horizontal and vertical threads. However, it could be made from little ceramic tiles (and black grout).