Jackson Pollock: Fractal Dimensions

From "The Aesthetic Brain" by Anjan Chatterjee, "...The physicist Richard Taylor determined that Jackson Pollock's early paintings have "fractal dimensions" of around 1.45 -- the dimensions found for many coastlines. Later, when the works became more complex and 'rich,' the fd climbed as high as 1.72. Studies have shown that most viewers prefer artificial images with a fd of 1.3 to 1.5 (neither too regular nor too random."

From the Wikispaces article "Fractals in Art":

"Jackson Pollock was a gifted Abstract Expressionist artist who had a talent for creating fractals. At first glance, his art seems like a random conglomeration of paint. Critics complained that Pollock's work was utterly insignificant and could be easily replicated by simply splattering paint on a canvas. 

However, through closer examination, each of Pollock's movements were deliberate, each paint drip carefully planned, to create a harmonious artwork.

Jackson Pollock

But how does one determine whether his work contains fractals? One way is to measure the degree of fractal dimension -- the measure of self-similarity - and "fractal displacement" -- the level of fractal dimension at different locations. 

Below is a graph a measurement of both of these properties of Pollock's painting, 'Number 14' through the use of the 'box-counting' method in which sections of Pollock's work is covered with a number of computer-generated squares (represented as N(L)). This is repeated with differing square sizes (represented as L). Using an equation linking N(L) and L, values for fractional dimension (represented as D) can be calculated and graphed. As seen by the graph, the D values are linear, but its gradient is what determines whether a pattern is fractal. 

The typical accepted fractal dimension value for natural fractal patterns range from 1.25 to 1.3. Analysis of the graph reveals that Number 14 has a fractal dimension value of 1.45, significantly larger than the accepted fractal dimension value and thus, more complex patterns.

Jackson Pollock

Measure of fractional dimension of Pollock's painting, 'Number 14'

Jackson Pollock

Perhaps what is more interesting is the method in which Pollock created fractals. He introduced chaos through two radical differences in the way he applied paint to canvas. First, Pollock did not limit his movement to his hand and arms but included his body, providing an entire range of different lengths in which paint appeared on the canvas. Second, he painted by allowing paint to drip from the brush. In conjunction with varying trajectories due to his body movement, he generated an unpredictable, chaotic motion. Over the years, Pollock perfected this dripping technique as seen by increasingly larger fractional dimensional values in his work. 

Below is his most fractal-heavy work, Blue Poles. With such a high fractal dimension (1.72), Pollock challenges the limits of what human eye can determine something as beautiful.

Pollock's painting, 'Blue Poles' (1952)"

Jackson Pollock