This paper presents a study of the generation, manipulation and use of visual representations in different episodes of scientific discovery. The study identifies a common set of transformations of visual representations underlying the distinctive methods and imagery of different scientific fields. The existence of common features behind the diversity of visual representations suggests a common dynamical structure for visual thinking, showing how visual representations facilitate cognitive processes such as pattern-matching and visual inference through the use of tools, technologies and other cultural resources. This dynamical model suggests a way of theorizing the interaction of cognitive, socio-cultural and technological aspects of science without losing sight of the essential contribution each makes to the processes of discovery. Whereas scientific work is often construed epistemically, as having the aim of improving the fit between theories and phenomena or culturally given notions of what counts as reality, this study shows that scientists use transformations to modify visual representations in ways that achieve other kinds of match: between a representation and the cognitive demands of a task (such as pattern matching or mental rotation) or between an emerging representation and the social need to communicate and negotiate new meanings in a context of culturally embedded conventions. By showing how images connect each of the overlapping contexts of scientific work the proposed model negotiates the sometimes contested boundary between cognitive and social aspects of science.