Visualisation involves making and manipulating images that convey novel phenomena, ideas and meanings. It is central to the intellectual objectives of almost every area of science. It is therefore surprising that we still lack an understanding of how visual thinking works. Examples from different sciences illustrate how scientists interpret and explain phenomena by actively manipulating those patternlike features of the world that lend themselves to structural representation, and vice versa. The ability to move between two, three and four dimensions structures both imagination and analysis, enabling scientists to vary the complexity of each visualisation as its function changes during the process of discovery and communication. These findings suggest that there is a widely used visual method that relates human cognitive abilities to imaging practices in the sciences and the arts.