Half a century ago, Stern discussed this attribute of an artistic object and called it apparency. While art is not limited to this single end, he felt that one of its two basic functions was "to create images which by clarity and harmony of form fulfill the need for vividly comprehensible appearance." In his mind, this was an essential first step toward the expression of inner meaning.
The personal experience of most of us will testify to this persistence of an illusory image long after its inadequacy is conceptually realized. We stare into the jungle and see only the sunlight on the green leaves, but a warning noise tells us that an animal is hidden there. The observer then learns to interpret the scene by singling out "give-away" clues and by reweighting previous signals. The camouflaged animal may now be picked up by the reflection of its eyes. Finally by repeated experience the entire pattern of perception is changed, and the observer need no longer consciously search for give-aways, or add new data to an old framework. They have achieved an image which will operate successfully in the new situation, seeming natural and right. Quite suddenly the hidden animal appears among the leaves, "as plain as day."
Everything points to the conclusion that the phrase 'the language of art' is more than a loose metaphor, that even to describe the visible world in images we need a developed system of schemata.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.