An algebra of pictures is described that is sufficiently powerful to denote the structure of a well-known Escher woodcut, Square Limit. A decomposition of the picture that is reasonably faithful to Escher’s original design is given. This illustrates how a suitably chosen algebraic specification can be both a clear description and a practical implementation method. It also allows us to address some of the criteria that make a good algebraic description.

We present in this paper a simple, device-independent model for describing two-dimensional graphics using a functional language. Graphical scenes, or pictures, are represented as values that functions can manipulate and inspect to create new values. Complete pictures are constructed by repeatedly composing such picture values together using picture combinators. A novel aspect of the model presented is its use of structured translation to abstractly express the geometric composition of arbitrary pictures. The structured graphics model presented has been implemented in Haskell, and we also give an overview of a general rendering framework for traversing a picture value. Applications of this renderer include both output to various graphical systems, testing for picking or selection of a picture and the computation of the bounding box of an arbitrary picture. The graphics model forms the basis for all graphical output in a user interface framework being developed in Haskell. 1 Introductio...