Tag Archives: fractals

Dendritic painting: a physics story

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.

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.

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.

Dynamic magnetic fractal networks for neuromorphic (brainlike) computing

Credit: Advanced Materials (2023). DOI: 10.1002/adma.202300416 [cover image]

This is a different approach to neuromorphic (brainlike) computing being described in an August 28, 2023 news item on phys.org, Note: A link has been removed,

The word “fractals” might inspire images of psychedelic colors spiraling into infinity in a computer animation. An invisible, but powerful and useful, version of this phenomenon exists in the realm of dynamic magnetic fractal networks.

Dustin Gilbert, assistant professor in the Department of Materials Science and Engineering [University of Tennessee, US], and colleagues have published new findings in the behavior of these networks—observations that could advance neuromorphic computing capabilities.

Their research is detailed in their article “Skyrmion-Excited Spin-Wave Fractal Networks,” cover story for the August 17, 2023, issue of Advanced Materials.

An August 18, 2023 University of Tennessee news release, which originated the news item, provides more details,

“Most magnetic materials—like in refrigerator magnets—are just comprised of domains where the magnetic spins all orient parallel,” said Gilbert. “Almost 15 years ago, a German research group discovered these special magnets where the spins make loops—like a nanoscale magnetic lasso. These are called skyrmions.”

Named for legendary particle physicist Tony Skyrme, a skyrmion’s magnetic swirl gives it a non-trivial topology. As a result of this topology, the skyrmion has particle-like properties—they are hard to create or destroy, they can move and even bounce off of each other. The skyrmion also has dynamic modes—they can wiggle, shake, stretch, whirl, and breath[e].

As the skyrmions “jump and jive,” they are creating magnetic spin waves with a very narrow wavelength. The interactions of these waves form an unexpected fractal structure.

“Just like a person dancing in a pool of water, they generate waves which ripple outward,” said Gilbert. “Many people dancing make many waves, which normally would seem like a turbulent, chaotic sea. We measured these waves and showed that they have a well-defined structure and collectively form a fractal which changes trillions of times per second.”

Fractals are important and interesting because they are inherently tied to a “chaos effect”—small changes in initial conditions lead to big changes in the fractal network.

“Where we want to go with this is that if you have a skyrmion lattice and you illuminate it with spin waves, the way the waves make its way through this fractal-generating structure is going to depend very intimately on its construction,” said Gilbert. “So, if you could write individual skyrmions, it can effectively process incoming spin waves into something on the backside—and it’s programmable. It’s a neuromorphic architecture.”

The Advanced Materials cover illustration [image at top of this posting] depicts a visual representation of this process, with the skyrmions floating on top of a turbulent blue sea illustrative of the chaotic structure generated by the spin wave fractal.

“Those waves interfere just like if you throw a handful of pebbles into a pond,” said Gilbert. “You get a choppy, turbulent mess. But it’s not just any simple mess, it’s actually a fractal. We have an experiment now showing that the spin waves generated by skyrmions aren’t just a mess of waves, they have inherent structure of their very own. By, essentially, controlling those stones that we ‘throw in,’ you get very different patterns, and that’s what we’re driving towards.”

The discovery was made in part by neutron scattering experiments at the Oak Ridge National Laboratory (ORNL) High Flux Isotope Reactor and at the National Institute of Standards and Technology (NIST) Center for Neutron Research. Neutrons are magnetic and pass through materials easily, making them ideal probes for studying materials with complex magnetic behavior such as skyrmions and other quantum phenomena.

Gilbert’s co-authors for the new article are Nan Tang, Namila Liyanage, and Liz Quigley, students in his research group; Alex Grutter and Julie Borchers from National Institute of Standards and Technology (NIST), Lisa DeBeer-Schmidt and Mike Fitzsimmons from Oak Ridge National Laboratory; and Eric Fullerton, Sheena Patel, and Sergio Montoya from the University of California, San Diego.

The team’s next step is to build a working model using the skyrmion behavior.

“If we can develop thinking computers, that, of course, is extraordinarily important,” said Gilbert. “So, we will propose to make a miniaturized, spin wave neuromorphic architecture.” He also hopes that the ripples from this UT Knoxville discovery inspire researchers to explore uses for a spiraling range of future applications.

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

Skyrmion-Excited Spin-Wave Fractal Networks by Nan Tang, W. L. N. C. Liyanage, Sergio A. Montoya, Sheena Patel, Lizabeth J. Quigley, Alexander J. Grutter, Michael R. Fitzsimmons, Sunil Sinha, Julie A. Borchers, Eric E. Fullerton, Lisa DeBeer-Schmitt, Dustin A. Gilbert. Advanced Materials Volume 35, Issue 33 August 17, 2023 2300416 DOI: https://doi.org/10.1002/adma.202300416 First published: 04 May 2023

This paper is behind a paywall.

Fractal brain structures and story listening

For anyone who needs to brush up on their fractals,

Caption: Zoomed in detail of the Mandelbrot set, a famous fractal, at different spatial scales of 1x, 4x, 16x, and 64x (from left to right). Credit: Image by Jeremy R. Manning.

My September 3, 2012 posting (Islands of Benoît Mandelbrot: Fractals, Chaos, and the Materiality of Thinking exhibition opening in Sept. 2012 in New York) includes an explanation of fractals. There is another explanation in the news release that follows below.

The story

A September 30, 2021 Dartmouth College news release announces work from a team of researchers using the concept of fractals as a way of understanding how the brain works (Note: Links have been removed),

Understanding how the human brain produces complex thought is daunting given its intricacy and scale. The brain contains approximately 100 billion neurons that coordinate activity through 100 trillion connections, and those connections are organized into networks that are often similar from one person to the next. A Dartmouth study has found a new way to look at brain networks using the mathematical notion of fractals, to convey communication patterns between different brain regions as people listened to a short story.The results are published in Nature Communications.

“To generate our thoughts, our brains create this amazing lightning storm of connection patterns,” said senior author Jeremy R. Manning, an assistant professor of psychological and brain sciences, and director of the Contextual Dynamics Lab at Dartmouth. “The patterns look beautiful, but they are also incredibly complicated. Our mathematical framework lets us quantify how those patterns relate at different scales, and how they change over time.”

In the field of geometry, fractals are shapes that appear similar at different scales. Within a fractal, shapes and patterns are repeated in an infinite cascade, such as spirals comprised of smaller spirals that are in turn comprised of still-smaller spirals, and so on. Dartmouth’s study shows that brain networks organize in a similar way: patterns of brain interactions are mirrored simultaneously at different scales. When people engage in complex thoughts, their networks seem to spontaneously organize into fractal-like patterns. When those thoughts are disrupted, the fractal patterns become scrambled and lose their integrity.

The researchers developed a mathematical framework that identifies similarities in network interactions at different scales or “orders.” When brain structures do not exhibit any consistent patterns of interaction, the team referred to this as a “zero-order” pattern. When individual pairs of brain structures interact, this is called a “first-order” pattern. “Second-order” patterns refer to similar patterns of interactions in different sets of brain structures, at different scales. When patterns of interaction become fractal— “first-order” or higher— the order denotes the number of times the patterns are repeated at different scales.

The study shows that when people listened to an audio recording of a 10-minute story, their brain networks spontaneously organized into fourth-order network patterns. However, this organization was disrupted when people listened to altered versions of the recording. For example, when the story’s paragraphs were randomly shuffled, preserving some but not all of the story’s meaning, people’s brain networks displayed only second-order patterns. When every word of the story was shuffled, this disrupted all but the lowest level (zero-order) patterns.

“The more finely the story was shuffled, the more the fractal structures of the network patterns were disrupted,” said first author Lucy Owen, a graduate student in psychological and brain sciences at Dartmouth. “Since the disruptions in those fractal patterns seemed directly linked with how well people could make sense of the story, this finding may provide clues about how our brain structures work together to understand what is happening in the narrative.”

The fractal network patterns were surprisingly similar across people: patterns from one group could be used to accurately estimate what part of the story another group was listening to.

The team also studied which brain structures were interacting to produce these fractal patterns. The results show that the smallest scale (first-order) interactions occurred in brain regions that process raw sounds. Second-order interactions linked these raw sounds with speech processing regions, and third-order interactions linked sound and speech areas with a network of visual processing regions. The largest-scale (fourth-order) interactions linked these auditory and visual sensory networks with brain structures that support high-level thinking. According to the researchers, when these networks organize at multiple scales, this may show how the brain processes raw sensory information into complex thought—from raw sounds, to speech, to visualization, to full-on understanding.

The researchers’ computational framework can also be applied to areas beyond neuroscience and the team has already begun using an analogous approach to explore interactions in stock prices and animal migration patterns.

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

High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns by Lucy L. W. Owen, Thomas H. Chang & Jeremy R. Manning. Nature Communications volume 12, Article number: 5728 (2021) DOI: https://doi.org/10.1038/s41467-021-25876-x Published: 30 September 2021

This paper is open access.

Energy storage inspired by a fern’s fractal patterns

Australian researchers have come up with a bio-inspired approach to making solar energy storage more viable according to a March 31, 2017 news item on Nanowerk (Note: A link has been removed),

Inspired by an American fern, researchers have developed a groundbreaking prototype that could be the answer to the storage challenge still holding solar back as a total energy solution (Science Express, “Bioinspired fractal electrodes for solar energy storages”).

The breakthrough electrode prototype (right) can be combined with a solar cell (left) for on-chip energy harvesting and storage. (Image: RMIT University)

A March 31, 2017 RMIT University press release, which originated the news item on Nanowerk, provides more detail (Note: A link has been removed),

The new type of electrode created by RMIT University researchers could boost the capacity of existing integrable storage technologies by 3000 per cent.

But the graphene-based prototype also opens a new path to the development of flexible thin film all-in-one solar capture and storage, bringing us one step closer to self-powering smart phones, laptops, cars and buildings.

The new electrode is designed to work with supercapacitors, which can charge and discharge power much faster than conventional batteries. Supercapacitors have been combined with solar, but their wider use as a storage solution is restricted because of their limited capacity.

RMIT’s Professor Min Gu said the new design drew on nature’s own genius solution to the challenge of filling a space in the most efficient way possible – through intricate self-repeating patterns known as “fractals”.

“The leaves of the western swordfern are densely crammed with veins, making them extremely efficient for storing energy and transporting water around the plant,” said Gu, Leader of the Laboratory of Artificial Intelligence Nanophotonics and Associate Deputy Vice-Chancellor for Research Innovation and Entrepreneurship at RMIT.

“Our electrode is based on these fractal shapes – which are self-replicating, like the mini structures within snowflakes – and we’ve used this naturally-efficient design to improve solar energy storage at a nano level.

“The immediate application is combining this electrode with supercapacitors, as our experiments have shown our prototype can radically increase their storage capacity – 30 times more than current capacity limits.

“Capacity-boosted supercapacitors would offer both long-term reliability and quick-burst energy release – for when someone wants to use solar energy on a cloudy day for example – making them ideal alternatives for solar power storage.”

Combined with supercapacitors, the fractal-enabled laser-reduced graphene electrodes can hold the stored charge for longer, with minimal leakage.

The fractal design reflected the self-repeating shape of the veins of the western swordfern, Polystichum munitum, native to western North America.

Lead author, PhD researcher Litty Thekkekara, said because the prototype was based on flexible thin film technology, its potential applications were countless.

“The most exciting possibility is using this electrode with a solar cell, to provide a total on-chip energy harvesting and storage solution,” Thekkekara said.

“We can do that now with existing solar cells but these are bulky and rigid. The real future lies in integrating the prototype with flexible thin film solar – technology that is still in its infancy.

“Flexible thin film solar could be used almost anywhere you can imagine, from building windows to car panels, smart phones to smart watches. We would no longer need batteries to charge our phones or charging stations for our hybrid cars.

“With this flexible electrode prototype we’ve solved the storage part of the challenge, as well as shown how they can work with solar cells without affecting performance. Now the focus needs to be on flexible solar energy, so we can work towards achieving our vision of fully solar-reliant, self-powering electronics.”

The repeating pattern of veins in the leaves of the western swordfern, as seen here magnified 400 times, served as the inspiration for the new high-density electrode(Credit: RMIT University)

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

Bioinspired fractal electrodes for solar energy storages by Litty V. Thekkekara & Min Gu. Scientific Reports 7, Article number: 45585 (2017) doi:10.1038/srep45585 Published online: 31 March 2017

This is an open access paper.

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

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.

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.

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).

Metallic nanoflowers produce neuron-like fractals

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.

A July 28, 2015 University of Oregon news release (also on EurekAlert) by Jim Barlow, which originated the news item, continues the patent celebration,

“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’,

FractalImplant

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.

You can find out more about InnoCentive here. As for other types of artificial eye implants, the latest here is a June 30, 2015 post titled, Clinical trial for bionic eye (artificial retinal implant) shows encouraging results (safety and efficacy).

Repeating patterns: earth’s daily rotation cycle seen in protein

This story made me think of fractals where a pattern at one scale is repeated at a smaller scale. Here’s more about the earth’s rotation and the protein from a June 25, 2015 news item on ScienceDaily,

A collaborative group of Japanese researchers has demonstrated that the Earth’s daily rotation period (24 hours) is encoded in the KaiC protein at the atomic level, a small, 10 nm-diameter biomolecule expressed in cyanobacterial cells.

For anyone who’s unfamiliar (me) with cyanobacteria, here’s a definition from its Wikipedia entry (Note: Links have been removed),

Cyanobacteria /saɪˌænoʊbækˈtɪəriə/, also known as Cyanophyta, is a phylum of bacteria that obtain their energy through photosynthesis.[3] The name “cyanobacteria” comes from the color of the bacteria (Greek: κυανός (kyanós) = blue). They are often called blue-green algae (but some consider that name a misnomer, as cyanobacteria are prokaryotic and algae should be eukaryotic,[4] although other definitions of algae encompass prokaryotic organisms).[5]

By producing gaseous oxygen as a byproduct of photosynthesis, cyanobacteria are thought to have converted the early reducing atmosphere into an oxidizing one, causing the “rusting of the Earth”[6] and dramatically changing the composition of life forms on Earth by stimulating biodiversity and leading to the near-extinction of oxygen-intolerant organisms. According to endosymbiotic theory, the chloroplasts found in plants and eukaryotic algae evolved from cyanobacterial ancestors via endosymbiosis.

The idea that cyanobacteria may have changed the earth’s atmosphere into an oxidizing one and stimulating biodiversity is fascinating to me. Plus, cyanobacteria are pretty,

    CC BY-SA 3.0     File:Tolypothrix (Cyanobacteria).JPG     Uploaded by Matthewjparker     Created: January 22, 2013     Location: 29° 38′ 58.2″ N, 82° 20′ 40.8″ W [downloaded from https://en.wikipedia.org/wiki/Cyanobacteria]

CC BY-SA 3.0
File:Tolypothrix (Cyanobacteria).JPG
Uploaded by Matthewjparker
Created: January 22, 2013
Location: 29° 38′ 58.2″ N, 82° 20′ 40.8″ W [downloaded from https://en.wikipedia.org/wiki/Cyanobacteria]

A June 26, 2015 Japan National Institute of Natural Sciences, which originated the news item, provides more information,

The results of this joint research will help elucidate a longstanding question in chronobiology: How is the circadian period of biological clocks determined? The results will also help understand the basic molecular mechanism of the biological clock. This knowledge might contribute to the development of therapies for disorders associated with abnormal circadian rhythms.

The results will be disclosed online on June 25, 2015 (North American Eastern Standard Time) in ScienceExpress, the electronic version of Science, published by the American Association for the Advancement of Science (AAAS).
1. Research Background

In accordance with diurnal changes in the environment (notably light intensity and temperature) resulting from the Earth’s daily rotation around its axis, many organisms regulate their biological activities to ensure optimal fitness and efficiency. The biological clock refers to the mechanism whereby organisms adjust the timing of their biological activities. The period of this clock is set to approximately 24 hours. A wide range of studies have investigated the biological clock in organisms ranging from bacteria to mammals. Consequently, the relationship between the biological clock and multiple diseases has been clarified. However, it remains unclear how 24-hour circadian rhythms are implemented.

The research group mentioned above addressed this question using cyanobacteria. The cyanobacterial circadian clock can be reconstructed by mixing three clock proteins (KaiA, KaiB, and KaiC) and ATP. A study published in 2007 showed that KaiC ATPase activity, which mediates the ATP hydrolysis reaction, is strongly associated with circadian periodicity. The results of that study indicated that the functional structure of KaiC could be responsible for determining the circadian rhythm.

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Figure 1  Earth and the circadian clock protein KaiC
2. Research Results

KaiC ATPase activity exhibits a robust circadian oscillation in the presence of KaiA and KaiB proteins (Figure 2). In the study reported here, the temporal profile of KaiC ATPase activity exhibited an attenuating and oscillating component even in the absence of KaiA and KaiB. A close analysis revealed that this signal had a frequency of 0.91 day-1, which approximately coincided with the 24-hour period. Thus, KaiC is the source of a steady cycle that is in tune with the Earth’s daily rotation.
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Figure 2  KaiC ATPase activity-time profile
To identify causal structural factors, the N-terminal domain of KaiC was analyzed using high-resolution crystallography. The resultant atomic structures revealed the underlying cause of KaiC’s slowness relative to other ATPases (Figure 3). “A water molecule is prevented from attacking into the ideal position (a black dot in Figure 3) for the ATP hydrolysis by a steric hindrance near ATP phosphoryl groups. In addition, this hindrance is surely anchored to a spring-like structure derived from polypeptide isomerization,” elaborates Dr. Jun Abe. “The ATP hydrolysis, which involves access of a water molecule to the bound ATP and reverse isomerization of the polypeptide, is expected to require a significantly larger amount of free energy than for typical ATP hydrolysis. Thus, the three-dimensional atomic structure discovered in this study explains why the ATPase activity of KaiC is so much lower (by 100- to 1,000,000-fold) than that of typical ATPase molecules.”

150626_en3.jpgFigure 3  Structural basis for steady slowness. The steric barrier prevents access of a water molecule to the catalytic site (indicated by a black dot).

The circadian clock’s period is independent of ambient temperature, a phenomenon known as temperature compensation. One KaiC molecule is composed of six identical subunits, each containing duplicated domains with a series of ATPase motifs. The asymmetric atomic-scale regulation by the aforementioned mechanism dictates a feedback mechanism that maintains the ATPase activity at a constant low level. The authors of this study discovered that the Earth’s daily rotation period (24 hours) is implemented as the time constant of the feedback mechanism mediated in this protein structure.

3. Technological Implications

KaiC and other protein molecules are capable of moving on short time scales, on the order of 10-12 to 10-1 seconds. This study provides the first atomic-level demonstration that small protein molecules can generate 24-hour rhythms by regulating molecular structure and reactivity. Lab head and CIMoS Director Prof. Shuji Akiyama sees, “The fact that a water molecule, ATP, the polypeptide chain, and other universal biological components are involved in this regulation suggests that humans and other complex organisms may also share a similar molecular machinery. In the crowded intracellular environment that contains a myriad of molecular signals, KaiC demonstrates long-paced oscillations using a small amount of energy generated through ATP consumption. This clever mechanism for timekeeping in a noisy environment may inspire development of highly efficient and sustainable chemical reaction processes and molecular-system-based information processing.”
4. Glossary

1) Clock protein
A clock protein plays an essential role in the circadian pacemaker. Mutations and deficiencies in clock proteins can alter the intrinsic characteristics of circadian rhythm.

2) ATP
Adenosine triphosphate is a source of energy required for muscle contraction and many other biological activities. ATP, a nucleotide that mediates the storage and consumption of energy, is sometimes referred to as the “currency of biological energy” due to its universality and importance in metabolism. ATP consists of an adenosine molecule bound to three phosphate groups. Upon hydrolysis, the ATPase releases one phosphate molecule plus approximately 8 kcal/mol of energy.

3) Polypeptide isomerization
Protein polypeptide main chains undergo isomerization on a time scale of seconds or longer; therefore, protein isomerization is one of the slowest biological reactions. Most functional protein main chains have a trans conformation, and a few proteins have a functional cis conformation.

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

Atomic-scale origins of slowness in the cyanobacterial circadian clock by Jun Abe, Takuya B. Hiyama, Atsushi Mukaiyama, Seyoung Son, Toshifumi Mori, Shinji Saito, Masato Osako, Julie Wolanin, Eiki Yamashita, Takao Kondo, & Shuji Akiyama. Science DOI: 10.1126/science.1261040 Published Online June 25 2015 (on Science Express)

This paper is behind a paywall.

Kudos to the person(s) who wrote the news release.

The glassy side of fractals

An April 24, 2014 news item on Nanowerk highlights a breakthrough in glass (wordplay intended),

Colorful church windows, beads on a necklace and many of our favorite plastics share something in common — they all belong to a state of matter known as glasses. School children learn the difference between liquids and gases, but centuries of scholarship have failed to produce consensus about how to categorize glass.

Now, combining theory and numerical simulations, researchers have resolved an enduring question in the theory of glasses by showing that their energy landscapes are far rougher than previously believed.

An April 23, 2014 Duke University news release by Erin Weeks (also on EurekAlert), which originated the news item, provides a diagram (am I the only one who thinks these resemble cow udders?) and more infotmation,

Glasses form when their molecules get jammed into fractal "wells," as shown on the right, rather than smooth or slightly rough wells (left). Photo credit: Patrick Charbonneau. Courtesy: Duke University

Glasses form when their molecules get jammed into fractal “wells,” as shown on the right, rather than smooth or slightly rough wells (left). Photo credit: Patrick Charbonneau. Courtesy: Duke University

“There have been beautiful mathematical models, but with sometimes tenuous connection to real, structural glasses. Now we have a model that’s much closer to real glasses,” said Patrick Charbonneau, one of the co-authors and assistant professor of chemistry and physics at Duke University.

One thing that sets glasses apart from other phase transitions is a lack of order among their constituent molecules. Their cooled particles become increasingly sluggish until, caged in by their neighbors, the molecules cease to move — but in no predictable arrangement. One way for researchers to visualize this is with an energy landscape, a map of all the possible configurations of the molecules in a system.

Charbonneau [Patrick Charbonneau, one of the co-authors and assistant professor of chemistry and physics at Duke University] said a simple energy landscape of glasses can be imagined as a series of ponds or wells. When the water is high (the temperature is warmer), the particles within float around as they please, crossing from pond to pond without problem. But as you begin to lower the water level (by lowering the temperature or increasing the density), the particles become trapped in one of the small ponds. Eventually, as the pond empties, the molecules become jammed into disordered and rigid configurations.

“Jamming is what happens when you take sand and squeeze it,” Charbonneau said. “First it’s easy to squeeze, and then after a while it gets very hard, and eventually it becomes impossible.”

Like the patterns of a lakebed revealed by drought, researchers have long wondered exactly what “shape” lies at the bottom of glass energy landscapes, where molecules jam. Previous theories have predicted the bottom of the basins might be smooth or a bit rough.

“At the bottom of these lakes or wells, what you find is variation in which particles have a force contact or bond,” Charbonneau said. “So even though you start from a single configuration, as you go to the bottom or compress them, you get different realizations of which pairs of particles are actually in contact.”

Charbonneau and his co-authors based in Paris and Rome showed, using computer simulations and numeric computations, that the glass molecules jam based on a fractal regime of wells within wells.

The new description makes sense of several behaviors seen in glasses, like the property known as avalanching, which describes a random rearrangement of molecules that leads to crystallization.

Understanding the structure of glasses is more than an intellectual exercise — materials scientists stand to advance from the knowledge, which could lead to better control of the aging of glasses.

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

Fractal free energy landscapes in structural glasses by Patrick Charbonneau, Jorge Kurchan,     Giorgio Parisi, Pierfrancesco Urbani & Francesco Zamponi. Nature Communications 5, Article number: 3725 doi:10.1038/ncomms4725 Published 24 April 2014

This paper is behind a paywall but there is a free preview available through ReadCube Access.

The Code; a preview of the BBC documentary being released in Canada and the US

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.

The latest invisibility cloak

Fractal Antenna Systems Inc. has released a video which demonstrates an invisibility cloak. From the Dec. 20, 2010 news item on Nanowerk,

The video conclusively shows that invisibility science has taken a huge leap with fractal design. Fractals are geometric patterns that have complex structure built from scaled repetition of a simple pattern. Fractals make up the cloak and its ‘object’ layer, producing a wideband invisibility that slipstreams microwaves around obstacles. The other side appears with good fidelity, without the detectable presence of the obstacle. Although a proof-of-concept of an invisibility cloak was shown in 2006 at Duke University, such non-fractal efforts had limitations. The Duke cloak worked in one narrow band, had many more cloaking layers, possessed a discernable shadow, and required the obstacle to already be hiding behind a mirror. All of those obstacles have been solved using fractals, in grids called fractal metamaterial, as the firm’s cloak reveals.

I located the 2006 video from Duke University,

It’s Fractal Antenna System’s ability to project a wideband invisibility cloak that distinguishes this effort from Duke’s (from the news item),

Notes the firm’s CEO and chief inventor Nathan Cohen: “In 2008, Chinese researchers said it was impossible to make a wideband invisibility cloak. We not only did it, but reduced the number of cloak layers, and, most importantly, made a cloak you can see out of. That means a sensor, for example, can be made to disappear into the background over a wideband, but still be able to see what’s outside. These attributes are really the ‘holy grail’ of cloak designs, and strongly point towards a bright future for invisibility science.”

The fractal cloak works at microwaves; radio waves used by cell phones and wireless devices. The technology directly applies to infrared, and with technology advances in nanotechnology, can be made to make visual light invisibility cloaks, although Cohen cautions that it will be many years before visual light invisibility cloaks are perfected. “Other researchers are still hiding objects behind mirrors. What’s the point of a cloak if you are already hiding behind a mirror?” asked Cohen.

As best as I can tell, the objects that are being cloaked are not visible to the human eye as they are measurable at the nanoscale. Here’s the Fractal Antenna Systems video (from YouTube),

The narrator seems to have some an unfortunate vocal habit, he overmodulates so some parts are a bit ‘sing-song’.