We connect the problem of finding a suitable programming paradigm for graphics with its role in the visualisation of conceptual representations - state-based models that can capture an experiential view of knowledge that arguably cannot be expressed in a logical or declarative framework. Conceptual representations are identified by selecting systems of observables, and analysing the functional dependencies through which they are indivisibly linked in change. Such representations have a particularly significant role to play in exploratory design - an activity that has a high profile in modern computing applications such as modelling and simulation for virtual reality, reactive systems and concurrent engineering.
Because it links programming and modelling, an object-oriented paradigm offers some support for conceptual representation, but the emphasis it places upon object integrity, circumscription and encapsulation is in general too restrictive. We introduce an alternative modelling paradigm - empirical modelling - that is well-suited for conceptual representation in exploratory design, and outline its application to modelling the requirement for a computer-assisted jigsaw assembly environment. In this way, we illustrate the use of a software environment, incorporating three definitive (definition-based) notations for specifying graphical displays, that we have developed to construct and visualise conceptual representations.