1. A halftone screen represented by data stored in a data storage system, the halftone screen being compatible with a multilevel halftoning process and comprising: a first plurality of screen dot nuclei, each of the first plurality of screen dot nuclei existing in each of a first plurality of planes of the halftone screen, and each of the first plurality of screen dot nuclei maintaining a same or substantially a same location in each of the first plurality of planes; and a first plurality of screen dot peripheral regions, each bordering or surrounding a corresponding screen dot nucleus of the first plurality of screen dot nuclei, wherein each of the first plurality of planes is associated with one or more input intensity values.