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

"Jackson Pollock: Blind Spots" Blockbuster Show at the DMA

Dallas Museum of Art to Present Largest Exhibition Of Jackson Pollock’s Black Paintings Ever Assembled

Exhibition of Jackson Pollock’s Black Paintings to Open Exclusively at Dallas Museum of Art in November

Jackson Pollock: Blind Spots Is Only the Third Major U.S. Museum Exhibition to Focus Solely on the Artist

On November 20, 2015, the Dallas Museum of Art will present what experts have deemed a “once in a lifetime” exhibition, organized by the DMA’s Hoffman Family Senior Curator of Contemporary Art Gavin Delahunty: the largest survey of Jackson Pollock’s black paintings ever assembled.

This exceptional presentation will include many works that have not been exhibited for more than 50 years, several of which were considered lost. 

Jackson Pollock: Blind Spots offers critical new scholarship on this understudied yet pivotal period in the artist’s career and provides radical new insights into Pollock’s practice.

On view at the DMA through March 20, 2016, the exhibition will receive its sole US presentation in Dallas, with more than 70 works, including paintings, sculptures, drawings, and prints.

Jackson Pollock: Blind Spots is the first large-scale exhibition to be curated by Gavin Delahunty at the DMA since he joined the Museum in May 2014. The exhibition is co-organized with Tate Liverpool, where Delahunty previously served as Head of Exhibitions and Displays. Tate Liverpool opened a smaller version of the exhibition in June.

The exhibition will first introduce audiences to Pollock’s work via a selection of his classic drip paintings made between 1947 and 1950, including Number 2, 1950, a work from the Harvard Art Museums’ collection that has not traveled in over 20 years. 

These works will serve to contextualize the radical departure represented by the black paintings, a series of black enamel paintings that Pollock created between 1951 and 1953. An unprecedented 31 black paintings will be included in the DMA presentation, nearly double the next largest survey of these works (which was presented at the Museum of Modern Art in 1967).

 “While several of Jackson Pollock’s contemporaries combined black and white, his black paintings were exceptional in their absolute merging of color and surface, which went over and above what Pollock himself had previously achieved; this is a crucial difference for many contemporary artists revisiting Pollock’s work today,” said Delahunty. “Through a comprehensive display of more than 70 works, the exhibition offers the opportunity to address ‘blind spots’ in the current understanding of the artist’s practice, offering a new perspective on his lasting contributions to post-war and contemporary art.

“As one of the first American museums to acquire Pollock’s work, it only is fitting that the DMA should present this definitive exhibition of the black paintings, engaging a new generation of audiences with this important and under-examined aspect of the artist’s practice,” Delahunty concluded.

Also featured in the exhibition are 30 works on paper made by Pollock during the same period as the black paintings. Made with enamel and ink and watercolor, the works on paper are considered by scholars to be the artist’s most important as a draftsman. 

The exhibition will also feature five of Pollock’s extant six sculptures, which provide a true three-dimensional experience of his well-known painting approach. Together with the 37 paintings on view, these works immersive audiences in Pollock’s complete oeuvre and shed new light on the experimentation and ingenuity that has become synonymous with his practice. 

While Jackson Pollock’s leading role in the Abstract Expressionist movement has been widely discussed, less attention has been devoted to his black paintings period. In describing this pivotal phase in Pollock’s artistic trajectory, the critic and historian Michael Fried remarked that “[Pollock is] on the verge of an entirely new and different kind of painting . . . of virtually limitless potential.” The black paintings assembled for the exhibition will include significant loans from U.S., Asian, and European collections, as well as important works drawn from the collections of the DMA and Tate.

“Pollock's extraordinary, still controversial black paintings of 1951 finally get the attention they deserve; they prove to be just as radical as his earlier, more celebrated all-over drip paintings, and speak even more to our own time as well,” said John Elderfield, Chief Curator Emeritus of Painting and Sculpture, Museum of Modern Art.

Exhibition Organization and Tour:

Jackson Pollock: Blind Spots is co-organized by the Dallas Museum of Art and Tate Liverpool. The exhibition is curated by Gavin Delahunty, Hoffman Family Senior Curator of Contemporary Art, Dallas Museum of Art (formerly Head of Exhibitions and Displays at Tate Liverpool), with Stephanie Straine, Assistant Curator, Tate Liverpool. 

The exhibition is co-presented by Bank of America and Texas Instruments. Additional support is provided by The Pollock-Krasner Foundation, Inc.  The presentation in Dallas is made possible by TWO X TWO for AIDS and Art, an annual fundraising event that jointly benefits amfAR, The Foundation for AIDS Research and the Dallas Museum of Art, and the Contemporary Art Initiative.  Marketing support is provided by the Dallas Tourism Public Improvement District and the Dallas Convention & Visitors Bureau and Texas Monthly.

The exhibition tour includes:

Tate Liverpool: June 30–October 18, 2015

Dallas Museum of Art: November 20, 2015–March 20, 2016