Three summers ago, my friend Wei Wei taught me how to play mahjong, a popular Chinese tile-based game. I also drew inspiration from the small tiles used to create Roman mosaics - I must have had those on my mind because I often work with a (differently-spelled) software called Mosaiq.
My initial approach was to create evenly-spaced columns of rectangles. The first column would contain one rectangle, spanning the entire height; the second would contain two rectangles; the third, three; etc. Color-wise, I first wanted to have each rectangle's hue be correlated with its y-position, but I abandonded this approach in favor of a gradient between two colors instead. That covered the hue -- the saturation increased from left to right independent of hue.
Then, I applied a series of transformations in which I 1) divided the image into n columns and flipped every other one, 2) reflected the image over the line y = x or y = -x, and 3) rotated the center of the image by 45 or 90 degrees.