Picture Languages Generated by Assembling Tiles

We propose a new formalism for generating picture languages based on an assembly mechanism of tiles, that uses rules having a context and a replacement site. More precisely, a picture language will be generated from a finite set of initial pictures by iteratively applying rewriting rules from a given finite set of rules, called a tiling rule system (TRuS system). We prove that the TRuS systems have a greater generative capacity than the tiling systems of Giammarresi and Restivo. even in the case of one-letter alphabet picture languages. This is due mainly to the use of the notion of replacement.