Even though non-linearity is said to drive the behaviour of system dynamics models, modellers do not have access to techniques that show this happening. The tools at their disposal to present model structure are powerful, but, by nature, static. Formal model analysis methods has made significant progress in explaining how structure drives behaviour, but the connection to standard model conceptualisation techniques have generally not yet been made. This paper presents work that links the results of recent formal model analysis techniques to traditional conceptual diagramming techniques. A prototype visualisation tool is used to create dynamic causal diagrams that display the changing influences of the elements of model structure over a simulation run; it shows the waxing and waning of the influence of different sets of loops.