Applying formal picture languages to procedural content generation

Procedural content generation for games often uses tile sets. Tilings generated with tile sets are equivalent to pictures generated from a fixed alphabet of characters such as those explored in the area of vision. Formal languages over pictures and their methods of definition such as 2D regular expressions, automata, and array grammars are directly applicable to generation of tilings using finite tile sets. Though grammars such as string grammars, L-systems, and graph grammars have been explored and found useful for the definition of certain content, formal methods have mostly been ignored. We introduce 2D regular expressions and array grammars as generators. We reason about the theoretical capability of these constructs and develop some practical use cases for their application in procedural content generation for games. One area lacking with a search based approach to procedural content generation is an enumeration of all possible tilings that can be generated. We show that 2D regular expressions can be used for enumeration.