Bag context shape grammars

Shape grammars have become established as a method of generating designs (images), especially in architecture, engineering and product design. Most shape grammar systems generate images in a way that is not always regulated. This is because they are context free. As such, the application of their rules is not always controlled. In this paper, we introduce Bag Context Shape Grammars (BCSGs), for the generation of images in a regulated manner. The BCSGs are also context free, but the application of a rule is controlled by a special vector of integers called the bag, which changes during a derivation. This paper goes on to prove that every puzzle grammar with permitting features can be converted to a Bag Context Shape Grammar (BCSG). Further, it demonstrates the conversion process with examples. Additionally, this paper considers a set of images and demonstrates that BCSGs can generate a set of images with fewer variables and rules. These BCSGs could offer a wide range of application areas such as the generation of distractor (similar) images for visual password systems or scheme.