Jackson Pollock’s FractalsGeorgie Greenwood, Jakub Polák, Liam Turner, Siobhan Weekes

Introduction

In 1999, Richard Taylor made a boldclaim: that the drip paintings created by thelate, great Jackson Pollock contained frac-tal patterns so unique, that they could beemployed when testing paintings for authen-ticity.

Pollock’s Technique

To explain why fractals may be presentin Pollocks’ work, it would first be helpful tounderstand how the paintings were created.Pollock was nicknamed “Jack the Dripper”in 1956 by Time magazine due to his use of adrip painting technique, which he employedwhile standing over a large canvas, usuallyseveral feet in both length and width, placedflat on the ground. By constantly movingaround the canvas with a near-continuousstream of paint pouring onto it, Pollock ap-peared to be following Lévy flight.

Lévy Flight

Lévy flight can be defined as a se-quence of steps, each made in isotropicrandom directions (meaning that theyfollow a uniform distribution), with eachstep having a random length. Examplesof Lévy flight include the way animalsforage when food is scarce. Lévy flightis heavily related to chaos theory, a rela-tionship also shared by fractals.

Why Might We See Fractals?

Pollock’s “chaotic” movement around thecanvas appeared to imitate the chaos foundin nature, leading to similar types of patternsbeing generated. In the same way that onebranch on a tree may have the same struc-ture of the tree as a whole, some of Pollock’spaintings also displayed these fractal proper-ties.

Figure 1: Blue Poles (original title: Number 11, 1952)by Jackson Pollock. (Source: national gallery of aus-tralia)

Taylor also argued that the lasting ap-peal behind Pollock’s paintings was due tofractal patterns, which people may naturallyfind aesthetically pleasing. After conduct-ing a series of polls, Taylor concluded thatpeople seem to prefer artwork with fractaldimensions similar to those found in nature.

If Pollock’s artwork did contain exam-ples of truly complex fractals as Taylor sug-gested, then further exploration could yieldan answer to the question of how to dis-tinguish forgeries from the real thing - avital technique for the art community.

Measuring Pollock’s Fractals

In order to measure the fractal dimension(called DS) of Pollock’s paintings, the boxcounting method was used. This methodworks by covering the painting with a gridof identically sized squares and the numberof these squares which contain part of thepainted pattern is counted, denoted N(L).The length of these squares is reduced sys-tematically with the process repeated to findN(L) for various lengths, L.

The largest size L is taken at the sizeof the canvas, with the smallest at the sizeof the finest paintwork in the picture, ap-proximately 1mm. Fractal behaviour is ob-served when N(L) ∝ LD, where D is thebox counting dimension and 1 < D < 2,since the paintings are in two dimensions.These values of D are found by plotting agraph of logN(L) against logL and takingthe gradient of the resulting graph.

Figure 2: Untitled 5, the freehand drawing created byJones-Smith to counter Taylor’s argument. (Source:The New York Times)

Credibility of FractalAnalysis

Doubt about how viable fractals could bewhen testing Pollock paintings grew whenKatherine Jones-Smith and Harsh Mathurproved that the fractal-like behaviour canbe easily recreated, even by drawing free-hand. Jones-Smith found that simple draw-ings, such as the one in Figure 2, exhibitedthe same fractal behaviour that Pol-lock’s work did. Not only that, but testingsome of Pollock’s other paintings using frac-tal analysis also gave different results, whichwould imply that artwork known to be gen-uine were in fact forgeries.

Bibliography

[1] R. P. Taylor, A. P. Micolich, D. Jonas, Nature399, 422, 1999,http://www.nature.com/nature/journal/v444/n7119/full/nature05398.html.

[2] J. Ouellette, Discover Magazine, 1st November2001, http://discovermagazine.com/2001/nov/featpollock.

[3] R. P. Taylor, A. P. Micolich, D. Jonas, PhysicsWorld Volume 12, October 1999,https://plus.maths.org/content/fractal-expressionism.

(All accessed November 29th.)