The Little Children of Stonehenge: Variability Aught the Machine
More complex kinds of interactivity are also possible in which both the elements and the structure of the whole object are either modified or generated on the fly in response to the user's interaction with a program. We can refer to such implementations as open interactivity to distinguish them from the closed interactivity that uses fixed elements arranged in a fixed branching structure.
As long as there exists some kernel, some structure, some prototype that remains unchanged throughout the interaction, open interactivity can be thought of as a subset of the variability principle. Here a useful analogy can be made with Wittgenstein's theory of family resemblance, later developed into the theory of prototypes by cognitive psychologists. In a family, a number of relatives will share some features, although no single family member may possess all of the features. Similarly, according to the theory of prototypes, the meanings of many words in a natural language derive not through logical definition but through proximity to a certain prototype.