What you describe as “elegance” has been defined, using different terminology, by many different thinkers in different domains over the years. In each case, we’re talking about an emotional or affective coefficient of aesthetic experience. And in each case “elegance” is a function primarily of two variables: (1) the amount and variety of raw data in a given stimulus, and (2) the ease with which that data can be encoded by the observer.

The philosopher Robert Nozick describes what he calls “organic unity” as being the sine qua non of aesthetic experience. Works of art have higher organic unity the more they can create a harmonized, coherent experience over a larger number of dimensions (eg color, space, shading, shapes, etc).

Dan Sperber and Deirdre Wilson, in the book Relevance: Communication and Cognition, describe the quality of “relevance” in any form of communication, whether a scientific paper or a poem, as a function of quantitative and qualitative effects of a communication on the inferences available to our minds, discounted by the cognitive effort needed to process the communication.

Finally, the computer scientist Juergen Schmidhuber has written several papers about designing AI capable of creating aesthetically pleasing art, and what this has taught him about what humans find beautiful and interesting, and why. For Schmidhuber there is in important difference between beauty and interestingness.

The beauty of an object is a function of our ability to encode relevant data with the least amount of effort. Hence symmetrical faces are more beautiful, because faces are relevant to a social being, and symmetrical ones are easier to encode. Note the similarity to Nozick’s theory of organic unity.

Interestingness, on the other hand, is a function of the impact of a given data stream on the cognitive module responsible for encoding data of that type. A data stream that works a greater change on a given module at a lower processing cost is considered more interesting. Note the similarity to Sperber and Wilson’s theory of relevance.

I’d check out all these folks, and while I’m here I might as well add that I dedicated a whole chapter of my book Truth Evolves to this issue, where I summarized in greater depth all the thinkers I’ve cited here.