Visualisation is a semiotic process
Models are constructed in order to help one to understand a theory and its relevance to the world. Visual models are just one kind of model; other kinds may occur in other modalities such as hearing (`A cock crows like this: ``Cock-a-doodle-doo!'' '), taste (as in a wine-tasting, where one assumes that a sample will taste just as good at home, and even better at a later date), smell (as in a scent sample, again based on an assumption that it will smell at least as good in company as in the shop), touch (as in a sample of cloth, or in a test-drive of a car).
The basic semiotic property of a model is that it is iconic, i.e. it shares some properties with whatever it illustrates. A model necessarily differs in other properties from what it illustrates, for example in terms of size, material, weight, loudness.
In many respects, speech and writing are used in modelling the world. Bühler distinguished between the expressive, descriptive and appellative functions of language. The descriptive function be understood as the use of language to evoke and communicate a speaker's `mental model' of reality to a hearer.
From this point of view, the metalanguages of linguistics contain a part which is a model, namely object language representations. From this perspective, phonetic representations, feature structures, syntax trees are all models.
Theories and models:
In systematic terms, the following relations hold between theories and models.