The structure of paintings: formal grammar and design

Although substantial literature exists on the properties of formal grammars, much less has been written on the use of grammars for describing the languages which they are capable of explaining, Thus we see a well-developed theory concerning the expressive (generative) power of different kinds of formal grammars and powerful algorithmic methods (analytical) for the languages defined by these grammars. For natural spoken and written languages, grammars have been used for explaining their structure but for the two-dimensional generalization to designs, pictures, images, and fine arts, which has been known since 1964, almost no use has been made of grammars.The purpose of this paper is to call attention to the powerful dormant tools that can be used in the design arts. Some of the benefits of using these tools for describing existing (natural) design languages are discussed. How such uses may direct us from the more formal design arts into the fine arts is discussed by reporting progress on building a grammar for a class of contemporary paintings.