Halliday & Matthiessen (1999: 33-4):
The theoretical model makes considerable demands on the representational system or systems in which it is realised. Such a system must be able to handle the axial differentiation of the meaning base so that it represents not only structural configurations but also variation in delicacy, the indeterminacy between options in meaning, the move in instantiation from potential to instance, and other theoretical specifications. …
As we have already noted, the representational semiotic may also be language itself — the theory may be represented discursively in the register(s) of linguistics. In this case, the relationship between theory and language is similar to … a relationship where theory might be construed as a connotative semiotic (in Hjelmslev's, 1943, conception: a semiotic system whose expression plane is a semiotic system) …
Finally, the representational semiotic may also be a diagrammatic one — e.g. network graphs, tree diagrams, our circle diagrams. With such graphic representation, it is important to ask (i) if the information represented graphically can be restated in some other form of representation and (ii) if its realisational relationship with respect to theory is clear. There is a certain danger that the graphic representation is simply assumed to be natural and transparent even though it depends as much on semiotic conventions as any other system. Our own experience with circle diagrams is that, unless the representational convention has been made explicit, readers favour certain types of meaning: the circles are interpreted in terms of 'extension' rather than in terms of 'elaboration' — which is to say, they are read in constituency terms rather than in realisational terms. In any case, diagrams will only serve us as 'visualisations' as long as they construe a metaphor of abstract space at the theoretical stratum.