# Painting Mathematics

### Fractal analysis of Jackson Pollock’s art

Six years ago, whilst on sabbatical in England, Taylor realized his academic background of fractal analysis could be applied to Pollock’s work. Have you ever looked at a Jackson Pollock masterpiece and thought: “I could do that”? After all it is just a bit of paint dripped onto a canvas, right? Well, you wouldn’t be alone. Professor Richard Taylor, Director of the Materials Science Institute at the University of Oregon has had that thought too, although he believes those drip paintings are much more complex than they appear at first sight.

When viewing some of the drip paintings he began to postulate that there might be some hidden mathematics at play, and that might be why fake Pollock paintings can be picked out as forgeries with ease when compared with the original, and why some people find the originals breathtakingly beautiful.

As a result of that first idea, Taylor threw himself into study. Whilst working for an MA in Art History he poured over paintings, visited galleries and read art theory books which helped him confirm in his mind that what he was seeing in the Pollock’s was in fact complex mathematical theory brought to life. And then he set about making his own masterpiece.

A fractal, as we’ve mentioned before, is an infinitely repeating pattern. Some of these patterns exist only in mathematical theory, others can be understood in the physical world. Take a set of matryoshka dolls (sometimes called Russian dolls); each of these dolls fits inside a larger copy of itself, and could continue infinitely repeating that same pattern. This, in simple terms, is a fractal.

## Fractal analysis of the paintings

When looking at Pollock’s work, Professor Taylor found staggering examples of Pollock’s use or accidental inclusion of fractals (the artist, as far as we know, never commented on them). Taylor took 20 canvases from a nine-year period when Pollock was honing and perfecting his drip paintings. The physicist scanned photographic versions of the paintings (as some are now valued at more than \$30million he was unable to work with the originals). With these scanned versions Taylor used complex computer programs to divide the images into areas less than 2mm across. Looking at the images from this distance, Taylor concluded that the paintings contained similar fractal patterns to those found in nature.

It is one thing being able to painting simple fractal structures, but if you’ve ever seen a Pollock in a gallery (the Tate Modern in London has some, as does MoMA in New York) then you’ll know that the drip paintings are not simple. These large-scale paintings, sometimes many meters long, are complex and appear random. The idea that someone could have placed fractals into the painting, sometimes minute in their size, seems impossible. But to prove his theory that Pollock knew what he was doing, Taylor got out the paint brushes and went to work…

Using pendulums filled with paint, paintbrushes and other mediums, Taylor experimented with recreating Pollock’s style of painting. Using pictures of the artist at work, and anecdotal evidence, he was able to put together a painting style that mimicked to some extent that of the late-painter. He also invented a device he called the “Pollockizer”; this was a container of paint suspended from a frame, which could be moved and jolted by electromagnetic coils at the top of a string, connecting the paint vessel to the frame (a sort of controllable pendulum if you will). As the container moved, the vessel flung and threw paint onto the canvas below, as frequency changes and sizes of the movement to the string allowed for fractal and non-fractal patterns to be replicated on the canvas.

So although we’ve all probably thought that modern art is just a bunch of paint lobbed at a canvas, and arguably in some cases it is, what Taylor’s fractal analysis goes to show is that there are underlying patterns to some of the lobbed paint.

People prefer the visual appeal of fractals. That’s why the majority of us find an unexplainable beauty in nature, and why some architects strive to replicate those patterns in their work. But when it comes to art, and in particular Pollock’s drip painting, Taylor wanted to see if people had a preference to the fractals within the work.

He showed fifty people forty different examples of patterns found within Pollock’s work. Showing two examples at a time, Taylor asked the participants to pick their favorite pattern. Eighty percent of the time, participants were predisposed to the pattern displaying fractals.

So next time you are in a gallery, or a supermarket, or even just sat looking out the window, you could be finding beauty or distraction in the millions of fractals right there in front of your face; you just might not know it until you look a little closer.