Sudoku metrics

I’ve been experimenting with metrics for sudokus. For example, in the image above, each color occurs once as the center of a 3-by-3 block, four times as a corner, and four times as a side. There are also no instances of squares of the same color being adjacent diagonally, which is allowed by the sudoku rules is the squares are in different 3-by-3 blocks, but which visually makes the distribution of that color seem less random.
My thinking is that images with certain properties are more esthetically pleasing than other images. I have a computer program that generates sudokus, and I can plug in different metrics. The metrics also restrict the number of sudokus generated to more manageable levels. The image above is one of only 36, for example. Runs with less restrictive metrics go into the tens of millions.