Jackson Pollock’s work is often cited when fractal art is discussed. I think it’s largely because he likely produced the art without knowing about the concept.
No. 5, 1948 (Jackson Pollock, downloaded from Wikipedia essay about No. 5, 1948)
Richard Taylor, a professor of physics at the University of Oregon, provides more information about how fractals affect us and how this is relevant to his work with retinal implants in a March 30, 2017 essay for The Conversation (h/t Mar. 31, 2017 news item on phys.org), Note: Links have been removed),
Humans are visual creatures. Objects we call “beautiful” or “aesthetic” are a crucial part of our humanity. Even the oldest known examples of rock and cave art served aesthetic rather than utilitarian roles. Although aesthetics is often regarded as an ill-defined vague quality, research groups like mine are using sophisticated techniques to quantify it – and its impact on the observer.
We’re finding that aesthetic images can induce staggering changes to the body, including radical reductions in the observer’s stress levels. Job stress alone is estimated to cost American businesses many billions of dollars annually, so studying aesthetics holds a huge potential benefit to society.
Researchers are untangling just what makes particular works of art or natural scenes visually appealing and stress-relieving – and one crucial factor is the presence of the repetitive patterns called fractals.
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When it comes to aesthetics, who better to study than famous artists? They are, after all, the visual experts. My research group took this approach with Jackson Pollock, who rose to the peak of modern art in the late 1940s by pouring paint directly from a can onto horizontal canvases laid across his studio floor. Although battles raged among Pollock scholars regarding the meaning of his splattered patterns, many agreed they had an organic, natural feel to them.
My scientific curiosity was stirred when I learned that many of nature’s objects are fractal, featuring patterns that repeat at increasingly fine magnifications. For example, think of a tree. First you see the big branches growing out of the trunk. Then you see smaller versions growing out of each big branch. As you keep zooming in, finer and finer branches appear, all the way down to the smallest twigs. Other examples of nature’s fractals include clouds, rivers, coastlines and mountains.
In 1999, my group used computer pattern analysis techniques to show that Pollock’s paintings are as fractal as patterns found in natural scenery. Since then, more than 10 different groups have performed various forms of fractal analysis on his paintings. Pollock’s ability to express nature’s fractal aesthetics helps explain the enduring popularity of his work.
The impact of nature’s aesthetics is surprisingly powerful. In the 1980s, architects found that patients recovered more quickly from surgery when given hospital rooms with windows looking out on nature. Other studies since then have demonstrated that just looking at pictures of natural scenes can change the way a person’s autonomic nervous system responds to stress.
Are fractals the secret to some soothing natural scenes?Ronan, CC BY-NC-ND
For me, this raises the same question I’d asked of Pollock: Are fractals responsible? Collaborating with psychologists and neuroscientists, we measured people’s responses to fractals found in nature (using photos of natural scenes), art (Pollock’s paintings) and mathematics (computer generated images) and discovered a universal effect we labeled “fractal fluency.”
Through exposure to nature’s fractal scenery, people’s visual systems have adapted to efficiently process fractals with ease. We found that this adaptation occurs at many stages of the visual system, from the way our eyes move to which regions of the brain get activated. This fluency puts us in a comfort zone and so we enjoy looking at fractals. Crucially, we used EEG to record the brain’s electrical activity and skin conductance techniques to show that this aesthetic experience is accompanied by stress reduction of 60 percent – a surprisingly large effect for a nonmedicinal treatment. This physiological change even accelerates post-surgical recovery rates.
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Pollock’s motivation for continually increasing the complexity of his fractal patterns became apparent recently when I studied the fractal properties of Rorschach inkblots. These abstract blots are famous because people see imaginary forms (figures and animals) in them. I explained this process in terms of the fractal fluency effect, which enhances people’s pattern recognition processes. The low complexity fractal inkblots made this process trigger-happy, fooling observers into seeing images that aren’t there.
Pollock disliked the idea that viewers of his paintings were distracted by such imaginary figures, which he called “extra cargo.” He intuitively increased the complexity of his works to prevent this phenomenon.
Pollock’s abstract expressionist colleague, Willem De Kooning, also painted fractals. When he was diagnosed with dementia, some art scholars called for his retirement amid concerns that that it would reduce the nurture component of his work. Yet, although they predicted a deterioration in his paintings, his later works conveyed a peacefulness missing from his earlier pieces. Recently, the fractal complexity of his paintings was shown to drop steadily as he slipped into dementia. The study focused on seven artists with different neurological conditions and highlighted the potential of using art works as a new tool for studying these diseases. To me, the most inspiring message is that, when fighting these diseases, artists can still create beautiful artworks.
Recognizing how looking at fractals reduces stress means it’s possible to create retinal implants that mimic the mechanism.Nautilus image via www.shutterstock.com.
My main research focuses on developing retinal implants to restore vision to victims of retinal diseases. At first glance, this goal seems a long way from Pollock’s art. Yet, it was his work that gave me the first clue to fractal fluency and the role nature’s fractals can play in keeping people’s stress levels in check. To make sure my bio-inspired implants induce the same stress reduction when looking at nature’s fractals as normal eyes do, they closely mimic the retina’s design.
When I started my Pollock research, I never imagined it would inform artificial eye designs. This, though, is the power of interdisciplinary endeavors – thinking “out of the box” leads to unexpected but potentially revolutionary ideas.
I was a bit surprised to find that this University of Oregon story was about a patent. Here’s more from a July 28, 2015 news item on Azonano,
Richard Taylor’s vision of using artificial fractal-based implants to restore sight to the blind — part of a far-reaching concept that won an innovation award this year from the White House — is now covered under a broad U.S. patent.
The patent goes far beyond efforts to use the emerging technology to restore eyesight. It covers all fractal-designed electronic implants that link signaling activity with nerves for any purpose in animal and human biology.
Fractals are objects with irregular curves or shapes. “They are a trademark building block of nature,” said Taylor, a professor of physics and director of the Materials Science Institute at the University of Oregon [UO]. “In math, that property is self-similarity. Trees, clouds, rivers, galaxies, lungs and neurons are fractals. What we hope to do is adapt the technology to nature’s geometry.”
Named in U.S. patent 9079017 are Taylor, the UO, Taylor’s research collaborator Simon Brown, and Brown’s home institution, the University of Canterbury in New Zealand.
“We’re very delighted,” Taylor said. “The U.S. Patent and Trademark Office has recognized the novelty and utility of our general concept, but there is a lot to do. We want to get all of the fundamental science sorted out. We’re looking at least another couple of years of basic science before moving forward.”
The patent solidifies the relationship between the two universities, said Charles Williams, associate vice president for innovation at the UO. “This is still in the very early days. This project has attracted national attention, awards and grants.
“We hope to engage the right set of partners to develop the technology over time as the concept moves into potentially vast forms of medical applications,” Williams added. “Dr. Taylor’s interdisciplinary science is a hallmark of the creativity at the University of Oregon and a great example of the international research collaborations that our faculty engage in every day.”
Here’s an image illustrating the ‘fractal neurons’,
Caption: Retinal neurons, outlined in yellow, attach to and follows branches of a fractal interconnect. Such connections, says University of Oregon physicist Richard Taylor, could some day help to treat eye diseases such as macular degeneration. Credit: Courtesy of Richard Taylor
The news release goes on to describe the ‘fractal approach’ to eye implants which is markedly different from the implants entering the marketplace,
Taylor raised the idea of a fractal-based approach to treat eye diseases in a 2011 article in Physics World, writing that it could overcome problems associated with efforts to insert photodiodes behind the eyes. Current chip technology doesn’t allow sufficient connections with neurons.
“The wiring — the neurons — in the retina is fractal, but the chips are not fractal,” Taylor said. His vision, based on research with Brown, is to grow nanoflowers seeded from nanoparticles of metals that self assemble in a natural process, producing fractals that mimic and communicate with neurons.
It is conceivable, Taylor said, that fractal interconnects — as the implants are called in the patent — could be shaped so they network with like-shaped neurons to address narrow needs, such as a feedback loop for the sensation of touch from a prosthetic arm or leg to the brain.
Such implants would overcome the biological rejection of implants with smooth surfaces or those randomly patterned that have been developed in a trial-and-error approach to link to neurons.
Once perfected, he said, the implants would generate an electrical field that would fool a sea of glial cells that insulate and protect neurons from foreign invaders. Fractal interconnects would allow electrical signals to operate in “a safety zone biologically” that avoids toxicity issues.
“The patent covers any generic interface for connecting any electronics to any nerve,” Taylor said, adding that fractal interconnects are not electrodes. “Our interface is multifunctional. The primary thing is to get the electrical field into the system so that reaches the neurons and induces the signal.”
Taylor’s proposal for using fractal-based technology earned the top prize in a contest held by the innovation company InnoCentive. Taylor was honored in April [2015] at a meeting of the White House Office of Science and Technology Policy.
The competition was sponsored by a collaboration of science philanthropies including the Research Corporation for Science Advancement, the Gordon and Betty Moore Foundation, the W.M. Keck Foundation, the Kavli Foundation, the Templeton Foundation and the Burroughs Wellcome Fund.
The three episodes (Numbers, Shapes, and Prediction) of The Code, a BBC (British Broadcasting Corporation) documentary featuring Professor Marcus du Sautoy, focus on a ‘code’ that according to du Sautoy unlocks the secrets to the laws governing the universe.
During the weekend (June 16 & 17, 2012) I had the pleasure of viewing the two-disc DVD set which is to be released tomorrow, June 19, 2012, in the US and Canada. It’s a beautiful and, in its way, exuberant exploration of patterns that recur throughout nature and throughout human endeavours. In the first episode, Numbers, du Sautoy relates the architecture of the Chartres Cathedral (France) , St. Augustine‘s (a Roman Catholic theologian born in an area we now call Algeria) sacred numbers, the life cycle of the periodic cicada in Alabama, US and more to number patterns. Here’s an excerpt of du Sautoy in Alabama with Dr. John Cooley discussing the cicadas’ qualities as pets and their remarkable 13 year life cycle,
In the second episode, Shapes, du Sautoy covers beehive construction (engineering marvels), bird migrations and their distinct shapes (anyone who’s ever seen a big flock of birds move as one has likely marveled at the shapes the flock takes as it moves from area to another), computer animation, soap bubbles and more, explaining how these shapes can be derived from the principle of simplicity or as du Sautoy notes, ‘nature is lazy’. The question being, how do you make the most efficient structure to achieve your ends, i.e., structure a bird flock so it moves efficiently when thousands and thousands are migrating huge distances, build the best beehive while conserving your worker bees’ energies and extracting the most honey possible, create stunning animated movies with tiny algorithms, etc.?
Here’s du Sautoy with ‘soap bubbleologist’ Tom Noddy who’s demonstrating geometry in action,
For the final episode, Prediction, du Sautoy brings the numbers and geometry together demonstrating repeating patterns such as fractals which dominate our landscape, our biology, and our universe. du Sautoy visits a Rock Paper Scissors tournament in New York City trying to discern why some folks can ‘win’ while others cannot (individuals who can read other people’s patterns while breaking their own are more successful), discusses geographic profiling with criminal geographic profiler Prof. Kim Rossmo, Jackson Pollock’s paintings and his fractals, amongst other intriguing patterns.
I paid special to the Rossmo segment as he created and developed his geographic profiling techniques when he worked for the Vancouver (Canada) Police Department (VPD) and studied at a nearby university. As this groundbreaking work was done in my neck of the woods and Rossmo was treated badly by the VPD, I felt a special interest. There’s more about Rossmo’s work and the VPD issues in the Wikipedia essay (Note: I have removed links from the excerpt.),
D. Kim Rossmo is a Canadian criminologist specializing in geographic profiling. He joined the Vancouver Police Department as a civilian employee in 1978 and became a sworn officer in 1980. In 1987 he received a Master’s degree in criminology from Simon Fraser University and in 1995 became the first police officer in Canada to obtain a doctorate in criminology. His dissertation research resulted in a new criminal investigative methodology called geographic profiling, based on Rossmo’s formula.
In 1995, he was promoted to detective inspector and founded a geographic profiling section within the Vancouver Police Department. In 1998, his analysis of cases of missing sex trade workers determined that a serial killer was at work, a conclusion ultimately vindicated by the arrest and conviction of Robert Pickton in 2002. A retired Vancouver police staff sergeant has claimed that animosity toward Rossmo delayed the arrest of Pickton, leaving him free to carry out additional murders. His analytic results were not accepted at the time and after a falling out with senior members of the department he left in 2001. His unsuccessful lawsuit against the Vancouver Police Board for wrongful dismissal exposed considerable apparent dysfunction within that department.
… he moved to Texas State University where he currently holds the Endowed Chair in Criminology and is director of the Center for Geospatial Intelligence and Investigation. …
Within what appeared to be chaos, Rossmo found order. Somehow Jackson Pollock did the same thing to achieve entirely different ends, a new form of art. Here’s a video clip of du Sautoy with artist and physicist, Richard Taylor,
Intuitively, Pollock dripped paint onto his canvases creating fractals decades before mathematician, Benoit Mandelbrot, coined the phrase and established the theory. (I wrote previously about Jackson Pollock [and fluid dynamics] in my June 30, 2011 posting.)
I gather that du Sautoy’s ‘code’ will offer a unified theory drawing together numbers, patterns, and shapes as they are found throughout the universe in nature and in our technologies and sciences.
The DVDs offer three extras (4 mins. each): Phi’s the Limit (beauty and the golden ratio or Phi), Go Forth and Multiply (a base 2 system developed by Ethiopian traders predating binary computer codes by millenia) and Imagining the Impossible: The Mathematical Art of M. C. Escher (Dutch artist’s [Escher] experiments with tessellation/tiling).
I quite enjoyed the episodes although I was glad to have read James Gleick‘s book, Chaos (years ago) before viewing the third episode, Prediction and I was a little puzzled by du Sautoy’s comment in the first episode, Numbers, that atoms are not divisible. As I recall, you create an atomic bomb when you split an atom but it may have been one of those comments that didn’t come out as intended or I misunderstood.
You can find out more about The Code DVDs at Athena Learning. The suggested retail cost is $39.99 US or $52.99 CAD (which seems a little steep for Canadian purchasers since the Canadian dollar is close to par these days and, I believe, has been for some time).
In sum, this is a very engaging look at numbers and mathematics.
