Today we begin with information from a fractal analysis of Jackson Pollock’s paintings, take a look at fractals in general and specifically those of Mark Townsend, and end with Rose Rushbrooke’s quilted fractal art. This journey raises several questions.
In the late 1990s, Richard P. Taylor, a physicist at the University of New South Wales in Sydney, Australia, who is also trained as an artist, thought he recognized fractal qualities in Pollock’s paintings. According to Ivars Peterson (http://www.maa.org/mathland/mathtrek_9_20_99.html), online editor at Science News, (http://www.sciencenews.org), Taylor first applied this theory to Pollock’s painting Blue Poles, Number 11, 1952.
The painting was first photographed, and then the photos were scanned. Computer analysis of the color schemes and trajectories indicated Pollock’s patterns can be described as fractal. The resulting paper positing this process as a potential method for authentication purposes can be read at http://materialscience.uoregon.edu/taylor/art/TaylorSubmission.pdf.
In 2002, a cache of paintings was found in the belongings of one Alex Matter’s deceased parents. There was reason to think these might have been done by Jackson Pollock, and efforts were made to determine the authenticity of the paintings. Taylor was asked to give scientific input by applying his fractal analysis process. None of the found paintings exhibited the fractal characteristics of several of Jackson’s known paintings.
Katherine Jones-Smith and Harsh Mathur at Case Western Reserve University read a newspaper report of this, disagreed with the premise of fractal characteristics in Pollock’s paintings, and set out to refute the idea. Katherine proceeded to make what she deemed to be random scribbles. When analyzed mathematically, these scribbles were found to exhibit fractal dimensions. (http://www.sciencenews.org/articles/20070224/bob9.asp)
Here are some images for comparison.
The first is another of Pollock’s paintings, Full Fathom Five,
Several other images of his paintings can be found at http://www.artchive.com/artchive/P/pollock.html#images if you would like to view more than the two I’ve uploaded here.
Here are two fractal images by Mark Townsend, Synergy,
and Caricature, which are reminiscent of some of Pollock’s paintings.
In his most recent gallery at
http://www.fractalus.com/fdimentia/recent/index.html Mark has several fractal images that are reminiscent of Pollock’s paintings.
The third is the sample of Jones-Smith’s scribbles given in the Science News Online article mentioned above.
I’m not qualified to comment on the fractal nature of Pollock’s or Smith-Jones’ work, (Townsend’s ARE fractal images), but, personally speaking, I do not find her squiggles to have anything near the same essence as the constantly wandering lines in both Pollock’s and Townsend’s work, or of any other fractal artist’s work with which I am acquainted.
Now let’s take a look at the question “what is a fractal?” It might seem I should have placed this earlier in the narrative, but for those who might not be familiar with fractals it would be better to compare Pollock’s pre-fractal paintings with some modern fractal images rendered in a style similar to Pollock’s, before discussing fractal structure.
The definition of fractals given by Jones-Smith and Mathur is very limited and rigid if not downright Euclidean, but fractal geometry, while mathematical, is much more fluid and difficult to pin down, non-Euclidian, generating ongoing debate among mathematicians and scientists about just what constitutes “fractal”.
A better (in my opinion) definition of fractals is this one found at http://www.fractalus.com/fractal-art-faq/faq03.html.
“A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale.”
And on this page http://www.fractalus.com/info/layman.htm is a description of fractals intended for anyone who has the urge to run from the room when math is mentioned.
Rose Rushbrooke also has an easy to grasp explanation of fractal geometry –“Fractal geometry is all the stuff which doesn’t have straight lines. Stuff in nature like clouds, trees, rocks, coastlines and sea shells. This is non-
Euclidian geometry.” http://www.roserushbrooke.com/about-fractals.html
If you are unfamiliar with fractals, http://www.fractalus.com hosts galleries for several very talented fractal artists, and has links to many informative sites. It’s worth the time to browse the site. Another excellent fractal art site is http://www.parkenet.org/jp/.
In the mid-1970s, Benoit Mandelbrot coined the term “fractal”, but the beginnings of fractal geometry occurred early in the 20th century when Swedish mathematician Helge von Koch developed the Koch Curve, a line segment that repeats infinitely.
The first image shows the Koch curve with four orders of magnitude. The line at the top with only one triangle jutting up is the first magnitude, the bottom one with the points so small they are beginning to become indistinct is the fourth order of magnitude. The second image shows the “snowflake” that results from joining three lines.
This webpage has a very good and understandable explanation of the fractal nature of the Koch curve to accompany the above illustrations, along with an animated zoom that shows the infinite repetition in continual progression.
Exploring fractal structures is next to impossible without the aid of computers to rapidly perform the necessary calculations. The addition of coloring algorithms in fractal generating applications increases the already vast possibilities of form available in fractal geometry, and gradients put color in the form. The computer age and advanced mathematics have given us fractal art, mathematics made visible. There is something about fractal structure that seems pleasing to the human eye.
The mandlebrot set is widely recognized as a classic fractal form.
Exploration of the mandelbrot set is the basis of much fractal art, but keep in mind that this is a vast oversimplification of things.
What does one do with a fractal after creating it? Fractal galleries abound in cyberspace. Fractal prints are available as posters and greeting cards, fractal images are printed onto t-shirts and other garments, used as illustrations for book and cd covers, and show up just about everywhere. Janet Parke sells fine art prints. Some of Kerry Mitchell’s fractals have been used to make textile prints. The list goes on and on.
Rose Rushbrooke creates original fractal images on her computer, and then translates her digital art into art quilts. Her work has been on display in many venues, and can be seen at http://www.roserushbrooke.com/fractal-art-quilts-1.html.
Rushbrooke is an accomplished artist in addition to her fractal art quilts, which can easily be seen by perusing her website (http://www.roserushbrooke.com), but it is her fractal art quilts that I want to examine in the context of today’s post.
Here are images of two of her fractal art quilts:
The Cliffs of Progress
Both are easily identifiable as explorations of the basic mandelbrot formula. The fractal nature of the artwork is accepted by the observer, without complex mathematical analysis or quibbling over what constitutes a fractal.
PART 4 Points for Discussion
“The modern artist is working with space and time and expressing his feelings rather than illustrating.” –Jackson Pollock
Given that Pollock lived a troubled and turbulent life, is it possible that he was illustrating his feelings at the same time he was expressing them, that the expression IS the illustration? What about abstract expressionism in general? If you think the expression is the illustration, does it also work in reverse – is representational art also an expression of feelings at the same time it illustrates? Are illustration and expression mutually exclusive or are there some gray areas?
“Every good painter paints what he is.” –Jackson Pollock
“My concerns are with the rhythms of nature…” –Jackson Pollock
“I am nature.” –Jackson Pollock
Would you agree that some of Pollock’s paintings contain fractal elements? If his drip and pour methods do exhibit fractal elements, might this be an unconscious expression of the fractal elements of nature? How do you see Pollock’s paintings as an expression of the man himself? Do you see your own artwork as an expression of yourself, your feelings, as illustrations, or as some combination of the two? Do you think fractal art reveals the artist?
The Science News Online article states that “There’s been substantial debate about how many orders of magnitude are necessary for something to properly be considered fractal.”
Might this debate call into question the fractal element in Rushbrooke’s fractal art quilts? Her work exhibits very few orders of magnitude, and yet most would agree it has fractal content. If Pollock’s work was analyzed with complex mathematics to determine fractal content, how would Rushbrooke’s quilts be analyzed? Other fractal art?
“It’s all a big game of construction, some with a brush, some with a shovel, some choose a pen.” –Jackson Pollock
“It doesn’t matter how the paint is put on, as long as something is said.” –Jackson Pollock
It seems all artists, even painters, must at some point justify themselves for existing as artists. Methods are often criticized, as was the case with Pollock. Each new technique, material and tool must fight an uphill battle to become accepted. Acrylic paints were at first somehow seen by some as a form of cheating because the artist no longer had to grind and mix her or his own pigments. Photography was not accepted as an art form for a long time. Art quilts and other forms of fiber art are still not always accepted as art. And we’ve entered the computer age, which allows the production of pleasing forms from mathematical formulae.
Fractal artists often hear the comment that “the computer did it.” But it still takes an artist’s eye to make good fractal art (and there is a lot of it out there that isn’t good), and one must learn how to mix light rays instead of paint using red, green, and blue instead of red, yellow, and blue. They must use principles of good composition and use computer applications instead of paintbrushes.
Fiber artists have heard criticisms of materials and tools meant to keep their art from being recognized as such.
How do you react to Pollock’s quotes above? How do you respond if someone says you are not making art because you use fabric, thread, etc? What do you think of the addition of computer as artist’s tool? Are there limits to what can be used as art materials or tools? Do methods, materials, and/or tools define what is art?