Tag Archives: fractal art

Dendritic painting: a physics story

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A March 4, 2024 news item on phys.org announces research into the physics of using paints and inks in visual art, Note: A link has been removed,

Falling from the tip of a brush suspended in mid-air, an ink droplet touches a painted surface and blossoms into a masterpiece of ever-changing beauty. It weaves a tapestry of intricate, evolving patterns. Some of them resemble branching snowflakes, thunderbolts or neurons, whispering the unique expression of the artist’s vision.

Okinawa Institute of Science and Technology (OIST) researchers set out to analyze the physical principles of this fascinating technique, known as dendritic painting. They took inspiration from the artwork of Japanese media artist, Akiko Nakayama. The work is published in the journal PNAS Nexus.

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Caption: Japanese artist Akiko Nakayama manipulates alcohol and inks to create tree-like dendritic patterns during a live painting session. Credit: Photo Credit: Akiko Nakayama

Yes, the ends definitely look tree-like (maybe cedar). A February 29, 2024 Okinawa Institute of Science and Technology (OIST) press release (also on EurekAlert but published March 1, 2024), which originated the news item, goes on to describe the forces at work and provides instructions for creating your own dendritic paintings, Note: Links have been removed,

During her [Akiko Nakayama] live painting performances, she applies colourful droplets of acrylic ink mixed with alcohol atop a flat surface coated with a layer of acrylic paint. Beautiful fractals – tree-like geometrical shapes that repeat at different scales and are often found in nature – appear before the eyes of the audience. This is a captivating art form driven by creativity, but also by the physics of fluid dynamics.

“I have a deep admiration for scientists, such as Ukichiro Nakaya and Torahiko Terada, who made remarkable contributions to both science and art. I was very happy to be contacted by OIST physicist Chan San To. I am envious of his ability ‘to dialogue’ with the dendritic patterns, observing how they change shape in response to different approaches. Hearing this secret conversation was delightful,” explains Nakayama.

“Painters have often employed fluid mechanics to craft unique compositions. We have seen it with David Alfaro Siqueiros, Jackson Pollock, and Naoko Tosa, just to name a few. In our laboratory, we reproduce and study artistic techniques, to understand how the characteristics of the fluids influence the final outcome,” says OIST Professor Eliot Fried of OIST’s Mechanics and Materials Unit, who likes looking at dendritic paintings from artistic and scientific angles.

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In dendritic painting, the droplets made of ink and alcohol experience various forces. One of them is surface tension – the force that makes rain droplets spherical in shape, and allows leaves to float on the surface of a pond. In particular, as alcohol evaporates faster than water, it alters the surface tension of the droplet. Fluid molecules tend to be pulled towards the droplet rim, which has higher surface tension compared to its centre. This is called the Marangoni effect and is the same phenomenon responsible for the formation of wine tears – the droplets or streaks of wine that form on the inside of a wine glass after swirling or tilting.

Secondly, the underlying paint layer also plays an important part in this artistic technique. Dr. Chan tested various types of liquids. For fractals to emerge, the liquid must be a fluid that decreases in viscosity under shear strain, meaning it has to behave somewhat like ketchup. It’s common knowledge that it’s hard to get ketchup out of the bottle unless you shake it. This happens because ketchup’s viscosity changes depending on shear strain. When you shake the bottle, the ketchup becomes less viscous, making it easier to pour it onto your dish. How is this applied to dendritic painting?

“In dendritic painting, the expanding ink droplet shears the underlying acrylic paint layer. It is not as strong as the shaking of a ketchup bottle, but it is still a form of shear strain. As with ketchup, the more stress there is, the easier it is for the ink droplets to flow,” explains Dr. Chan.

“We also showed that the physics behind this dendritic painting technique is similar to how liquid travels in a porous medium, such as soil. If you were to look at the mix of acrylic paint under the microscope, you would see a network of microscopic structures made of polymer molecules and pigments. The ink droplet tends to find its way through this underlying network, travelling through paths of least resistance, that leads to the dendritic pattern,” adds Prof. Fried.

Each dendritic print is one-of-a-kind, but there are at least two key aspects that artists can take into consideration to control the outcome of dendritic painting. The first and most important factor is the thickness of the paint layer spread on the surface. Dr. Chan observed that well-refined fractals appear with paint layer thinner than a half millimetre.

The second factor to experiment with is the concentration of diluting medium and paint in this paint layer. Dr. Chan obtained the most detailed fractals using three parts diluting medium and one part paint, or two parts diluting medium and one part paint. If the concentration of paint is higher, the droplet cannot spread well. Conversely, if the concentration of paint is lower, fuzzy edges will form. 

This is not the first science-meets-art project that members of the Mechanics and Materials Unit have embarked on. For example, they designed and installed a mobile sculpture on the OIST campus. The sculpture exemplifies a family of mechanical devices, called Möbius kaleidocycles, invented in the Unit, which may offer guidelines for designing chemical compounds with novel electronic properties.

Currently, Dr. Chan is also developing novel methods of analysing how the complexity of a sketch or painting evolves during its creation. He and Prof. Fried are optimistic that these methods might be applied to uncover hidden structures in experimentally captured or numerically generated images of flowing fluids.

“Why should we confine science to just technological progress?” wonders Dr. Chan. “I like exploring its potential to drive artistic innovation as well. I do digital art, but I really admire traditional artists. I sincerely invite them to experiment with various materials and reach out to us if they’re interested in collaborating and exploring the physics hidden within their artwork.”

Instructions to create dendritic painting at home

Everybody can have fun creating dendritic paintings. The materials needed include a non-absorbent surface (glass, synthetic paper, ceramics, etc.), a brush, a hairbrush, rubbing alcohol (iso-propyl alcohol), acrylic ink, acrylic paint and pouring medium.

  1. Dilute one part of acrylic paint to two or three parts of  pouring medium, or test other ratios to see how the result changes
  2. Apply this to the non-absorbent surface uniformly using a hairbrush. OIST physicists have found out that the thickness of the paint affects the result. For the best fractals, a layer of paint thinner than half millimetre is recommended.
  3. Mix rubbing alcohol with acrylic ink. The density of the ink may differ for different brands: have a try mixing alcohol and ink in different ratios
  4. When the white paint is still wet (hasn’t dried yet), apply a droplet of the ink with alcohol mix using a brush or another tool, such as a bamboo stick or a toothpick.
  5. Enjoy your masterpiece as it develops before your eyes. 

Here’s a link to and a citation for the paper,

Marangoni spreading on liquid substrates in new media art by San To Chan and Eliot Fried. PNAS Nexus, Volume 3, Issue 2, February 2024, pgae059 DOI: https://doi.org/10.1093/pnasnexus/pgae059 Published: 08 February 2024

This paper is open access.

Fractal imagery (from nature or from art or from mathematics) soothes

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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.

Fabulous essay, eh?

I have previously featured Jackson Pollock in a June 30, 2011 posting titled: Jackson Pollock’s physics and and briefly mentioned him in a May 11, 2010 visual arts commentary titled: Rennie Collection’s latest: Richard Jackson, Georges Seurat & Jackson Pollock, guns, the act of painting, and women (scroll down about 45% of the way).