We talk in this paper about using state machines and refinement to characterise the visualisation of a computation. We use Z specifications to give examples of systems in the usual way, and then use Z schemas to also represent states and transitions in state machines, which we consider to be a particular kind of visualisation of a specified system. We have investigated the principle of substitutivity and the idea of downward simulation to check whether or not a refinement relation exists between the specification and the state machine. We are looking at this because we believe that the soundness of the visualisation can be captured by such a refinement relationship.