Fractal and multifractal analysis is a natural way of identifying scale-invariant behavior manifest in seemingly random distributions. This provides a truly interdisciplinary tool with which one can study structures literally ranging from the extra-galactic realm of the cosmos to the psychophysical world of the canvas.
It has been shown that many works of art possess such hierarchical patterns. These are not only physically distributed on the canvas as blobs of paint, but also are resolved at various stages of visual processing. This phenomenon could help unlock the mechanisms of cognitive control during the painting process, and could moreover provide a method of identifying ar forgeries.
Related research papers: