A Mathematical Principle of Art and Human Vision

The study of visual illusions is an old subject and an important part of the psychology of human visual perception, but hitherto there has been no single principle able to explain radically different kinds of visual illusions conjointly. Such a principle does exist, as is to be shown: it is the mathematical theory of Fourier analysis. A great many visual illusions are what happen when the visual objects involved undergo certain frequency filtering, a concept derived from Fourier analysis. Phenomena thus explained belong in these distinct categories: brightness illusions, colour illusions, geometrical illusions, and motion illusions, all of which have been simulated with computer programs based on this mathematical principle. Visual illusions obeying this principle have in fact been depicted in Western painting for centuries, and examples from masterpieces abound. Thus it is a principle not only of human vision but also of fine art. What is more, art can in certain ways shed light on the quest for the understanding of human vision.