A process for producing paper webs having a pattern formed into the web is disclosed. The pattern is formed during formation of the web and is made by varying the basis weight of the web. The paper web is produced by depositing an aqueous suspension of fibers between two forming surfaces. One or both of the forming surfaces include lower permeability areas that create lower basis weight areas in the web. The lower permeability areas are contained in the forming surface according to a particular pattern. For instance, the lower permeability areas can be formed into a drainage roll sleeve contained on a drainage roll which contacts a forming surface. The drainage roll can be a forming roll or a breast roll.