Another way to add randomness to regular patterns is to use a technique called bombing. Bombing generates random placement patterns -- regular patterns or features which are "dropped" at random positions or orientations in texture space.
We start out with a regular pattern composed of diamonds (rotated squares).
Then using the bombing technique, we randomly move the position of each diamond. The key here, and the thing that distinguishes it from a perturbed regular pattern, is that the shifting is based on the tile coordinates (column & row of the tile) and not the texture coordinates. By using the tile coordinates as the seed (input) to noise, we get the same pseudo-random value (ouput) for every point inside that tile. And that's why the regular shape is maintained. If different random values are obtained within each tile, the diamond shapes will become irregular in shape.
To reiterate, the randomness must be based on tile coordinates (col,row) -- because (col,row) are constant for each tile -- and not on texture coordinates (ss,tt) or some other variable (e.g. s,t) which varies within each tile.
