1. A method performed, at least in part by one or more computers, for generating a multilevel halftone screen, the method comprising the steps of: receiving tile definition data describing a tile definition; generating a tile based at least upon the tile definition data, the tile having a plurality of screen dot nuclei; improving locations of the plurality of screen dot nuclei in the tile; and growing peripheral regions around each of the screen dot nuclei in each of a plurality of successive planes of the halftone screen.