A novel technique, the multiple ripple propagation technique, is presented for mapping and h*w grid into a w*h grid such that the dilation cost is 2, i.e. such that any two neighboring nodes in the first grid are mapped onto two nodes in the second grid that are separated by a distance of at most 2. The technique is then used as a basic tool for mapping any rectangular source grid into a square target grid with the dilation two property preserved. The ratio of the number of nodes in the source grid to the number of nodes in the target grid, called the expansion cost, is shown to be always less than 1.2. This is a significant improvement over the previously suggested techniques, where the expansion cost could be bounded by 1.2 only if the dilation cost was allowed to be as high as 18.>