The importance of Peirce's notion of diagram for his conception of scientific research is well known and cannot be understated. Diagrams are the kind of sign which allows us to "represent certain relations in such a form that it can be transformed into another form representing other relations involved in those first represented and this transformed icon can be interpreted in a symbolic statement" (MS [R] 339:286r).
But what is the nature of this transformation and of this symbolic expression? I will argue that it is a certain type of play, a game whose rules limit the acceptable ways of transforming diagrams and their symbolic expression, yet leave plenty of space for experimentation and therefore discovery of new scientific truths. Furthermore, I will discuss the relation of this game to what Peirce calls "Pure Play" (CP 6.458) and show that they are indeed very much alike.