Latest news with #CherryBlossoms'
New York Times
25-03-2025
- Sport
- New York Times
Washington Nationals City Connect uniforms, round two: What does our panel think?
The Washington Nationals, whose cherry blossom City Connect uniforms were No. 4 in The Athletic's rankings last season, announced their latest City Connect uniforms on Sunday. The new light blue uniform features an overlay of the city grid of Washington D.C., which the team calls an 'homage to the quadrants, grand avenues and even the traffic circles that connect us.' This year's edition, like its City Connext predecessor, features the District's famed cherry blossoms on the cap, as well as on the sleeve patch. The interlocking 'DC' on the chest — which was a part of the 2006-10 Nats uni — is stylized as a hat tip to the 1956 Washington Senators. Advertisement Washington's first attempt at a City Connect uniform — the gray and pink 'Cherry Blossoms' set — received much public acclaim, so creating its second version was always going be a bit of a tall task. When writers C. Trent Rosecrans, Stephen J. Nesbitt, Tyler Kepner and Jason Jones ranked the game's City Connects last year, all four had the Nationals in their top 10. How will the latest set fare? GO DEEPER MLB City Connect: All 29 uniforms ranked, from the so-so to the sublime C. Trent Rosecrans: As soon as the Nationals announced they were retiring the cherry blossom uniforms, it was clear they were likely in for a downgrade. That turned out to be true. But on its own, the new design is fine. It's probably still in the top half of the City Connect designs. Using the grid certainly connects the jersey to the city, so there's that. I also like that the cherry blossoms are still there and I think the cutout of the Capitol Dome inside the block 'W' gives the team one of its best looks. Aside from the near-perfect cherry blossom lid from the first edition, this new CC hat and its batting helmet and batting practice siblings are the best in the Nationals' wardrobe. Sure, having different designs for the hat, batting practice hat and the batting helmet is excessive, but all three are decent designs and better than any of the team's other looks. THE BLUEPRINT — Washington Nationals (@Nationals) March 23, 2025 Jason Jones: A blueprint of D.C. is certainly going all in on the City Connect theme. If there had to be a change, I like going completely away from last season's look It's still a top-tier alternative to the usual Washington uniform, even though I'm partial to the script 'W' over this block version on the cap. That W in this color would be one of the best in baseball, especially if there were no cherry blossoms on it (just my preference). But the detail on the W of incorporating the Capitol Dome is nice, so I'd still add it to my collection. The blueprint under the brim is an excellent detail that helps this look stand out even more. Advertisement The uniform still has pink details to accent the cool shades of blue. I like this more than last year's and that was a solid look for the Nationals. It might even be top-5 for me by the time the other new uniforms are revealed. Stephen J. Nesbitt: An absolute travesty. The Nationals' previous City Connect set was a beauty. This uniform stinks out loud. That was my immediate reaction after seeing this photo. I raced to my computer and typed out: 'This is a travel-ball team uniform that parents (rightfully) groused about having to shell out $150 for. The interlocking DC looking like the Perfect Game logo really drives that prep vibe home. The city grid is already almost unrecognizable given the grainy design, and under the noon sun, it'll just be an indistinct jumble of similar hues. It's a bad All-Star Game uniform in light blue.' Then I looked at some more photos and my Big Feelings calmed down. The new cap is cool, and I like the numbers on the back of the jersey. There are far worse City Connects. But I still much prefer the previous version, and second tries should be held to a high standard. Tyler Kepner: They don't really look like the Nats, though I understand that's often the point of the City Connect series. This worked well with the previous City Connect set because of the stylish pink splash from the cherry blossoms, which sadly have a minimal presence now. I really like how the outline of the Capitol Dome wedges into the W on the cap, though I don't understand why there's a different W on the helmet. Turning the whole jersey into a map is something new for a uniform, as far as I know, and it works. I like the sleeve patch, and I'll give them points for using the interlocking DC logo instead of the awkward 'WSH.' But while I'm really glad they went with white pants (blue-over-blue, as we see with the Twins, is a bad look), it's going to take a while to think 'Nationals' instead of 'Royals' when I see this uniform. If they'd used the light blue as part of an Expos motif, I might feel different, but these jerseys honor DC, not Montreal. All in all, a middle-of-the-pack outfit for a middle-of-the-pack team. (All photos courtesy of the Washington Nationals)
CNN
14-03-2025
- Science
- CNN
Trees in art, as well as life, often follow simple mathematical rules, study finds
Summary Scientists have discovered that trees in famous artwork follow the same mathematical fractal patterns as real trees. Researchers analyzed tree art across cultures, finding consistent branch scaling values matching those in nature. A University of New Mexico mathematical biologist says these patterns may help humans recognize stylized images as trees. In Mondrian's increasingly abstract tree paintings, the recognizability disappeared when fractal patterns were abandoned. Fractal patterns in art and nature are both functional and aesthetically pleasing, according to the study published in PNAS Nexus. Trees depicted in famous artworks across a range of styles follow the same mathematical rules as their real-life counterparts, scientists have found. The math concept hidden in this tree art — geometric shapes known as fractals — is apparent in branching patterns in nature and may be key to humans' ability to recognize such artwork as trees, according to Mitchell Newberry, a mathematical biologist at the University of New Mexico, and his colleague Jingyi Gao, a doctoral student at the University of Wisconsin. Like the branches, twigs and leaves of a tree, fractals repeat the same patterns across different scales. Snowflakes, lightning bolts and human blood vessels are also fractal structures, which all show a degree of self-similarity: As you zoom into the details of a fractal, you can see a replica of the whole. 'If you look at a tree, its branches are branching. Then the child branches repeat the figure of the parent branch,' Gao said in a news release. Newberry and Gao chose to study artworks depicting single trees. Their selections, which they said spanned different times and cultures, included 16th century stone window carvings from the Sidi Saiyyed Mosque in India, an 18th century painting called 'Cherry Blossoms' by Japanese artist Matsumura Goshun and two early 20th century works by Dutch painter Piet Mondrian. They also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). They found that the trees depicted in the artworks, even when abstract or stylistic, mostly, but not always, corresponded to branching patterns and scale found in natural trees. 'Any kind of abstraction is a way of trying to get at natural laws, whether it's a mathematical abstraction or an artistic abstraction. There's a lot of different kinds of trees in the world, but this theory shows us (and) gives us some baseline for what we expect a tree to be,' Newberry told CNN. Newberry said he had long been a fan of Mondrian's work and how the artist depicted trees in abstract ways, removing all but the most essential elements but still clearly conveying a tree. It jibed with his own work explaining mathematically how treelike structures in human biology such as veins and arteries and lungs use their physical form to efficiently deliver blood and air. To reach their findings, the researchers successfully came up with a method of assessing branching patterns in trees and generalized it into a simple common formula, according to Fabian Fischer, a researcher at Technical University of Munich in Germany who wasn't involved in Newberry and Gao's study. 'The method is based on ideas that go back to Leonardo da Vinci and have been revisited by biologists multiple times,' Fischer said. 'I found it a highly stimulating read, with an interesting connection between works of art and biology.' Scale of 1 to tree In nature, fractal patterns aren't just aesthetically pleasing, they're also often related to function. For example, branching enables trees to transport fluid, harvest light and maintain mechanical stability. Since a fractal is a geometric shape, mathematicians can calculate its complexity, or fractal dimension — even when it appears in art. 'There are some characteristics of the art that feel like they're aesthetic or subjective, but we can use math to describe it,' Gao said. In their research published in the scientific journal PNAS Nexus on February 11, Gao and Newberry analyzed the variation in the thickness of the tree branches in the artworks they studied. They took into account the number of smaller branches per larger branch and used this information to calculate a number they called the branch diameter scaling exponent. The study found that the trees in the artworks had a branch diameter scaling value broadly matching the 1.5 to 3 range for real trees. Outside those values, the objects depicted weren't easily recognizable as trees. Gao and Newberry were surprised to find the highly stylized Indian mosque carving had a value closer to real trees than the tree in 'Cherry Blossoms,' which they had initially thought was more natural-looking. Though extremely rich in detail, with over 400 individual branches, 'Cherry Blossoms' exhibited a scaling exponent of 1.4, while the pair calculated the Indian carved tree has a value of 2.5. Newberry said that having a more realistic branch diameter scaling factor may have enabled artists to take more creative risks yet still have the object recognizable as a tree. 'As you abstract away details and still want viewers to recognize this as a beautiful tree, then you may have to be closer to reality in some other aspects,' Newberry said. Of course, artists such as Mondrian and Klimt would likely not have been aware of fractals, or the math that underpins them, but perhaps had an innate understanding of the subtle proportions all trees share, according to the researchers. However, Fischer noted that the study was exploratory and the range of selected tree species and works of art is small and selective, therefore it's not possible to draw strong conclusions. Fractal pattern impacts The authors studied a series of works by abstract painter Mondrian that depict the same tree but in increasingly less realistic ways. His 1911 work 'De Grijze Boom' ('The Gray Tree') shows a series of black lines against a gray background, but the painting is nonetheless instantly recognizable as a tree, with its branch scaling value in the real tree range at 2.8. 'I don't think he (Mondrian) is even trying to find the essence of trees but as he's pulling things out, this thing that we think is really important in science ends up being one of the last things to go (away) in the art,' Newberry said. 'Clearly, he thinks it's really important, and clearly it's really important to human perception.' However, in Mondrian's 1912 'Bloeiende Appelboom' ('Blooming Apple Tree'), a painting in the same series, the branch diameter scaling is gone, Newberry said, with a value of 5.4. 'Whereas most viewers of Gray Tree immediately perceive a tree, naïve viewers of Blooming Apple Tree see dancers, roots, fish, faces, water, stained glass, leaves, flowers, or nothing representational at all,' the authors noted in the study. The researchers also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). Though the tree's depiction in this artwork is highly stylized, the study's measurements suggest it also fell into the statistical range of a real-life tree. The study authors are not the first to apply math to trees in art. Renaissance polymath Leonardo da Vinci observed tree growth and came up with his own mathematical rule for painting trees. His work on tree physiology inspired scientists and landscape artists alike to study branching patterns, according to the new research. The findings from the study are intriguing because they integrate artistic and scientific approaches to studying trees, said Richard Taylor, a professor of physics at the University of Oregon. 'Although focusing on trees, the article is tackling a much bigger question — why are natural patterns so beautiful — and interdisciplinary collaborations are essential for delivering the answers,' Taylor, who was not involved in the study, said via email. His research has focused on the positive impact of viewing fractal patterns in nature, which he said could reduce stress levels. 'Studies such as this one emphasize the aesthetic power of trees. There is a Japanese tradition known as 'forest bathing,' Taylor added. 'Based on studies such as these, a more appropriate description is 'fractal bathing.' We should soak up the aesthetic qualities of trees — whether this is in nature or in art.'
CNN
14-03-2025
- Science
- CNN
Trees in art, as well as life, often follow simple mathematical rules, study finds
Trees depicted in famous artworks across a range of styles follow the same mathematical rules as their real-life counterparts, scientists have found. The math concept hidden in this tree art — geometric shapes known as fractals — is apparent in branching patterns in nature and may be key to humans' ability to recognize such artwork as trees, according to Mitchell Newberry, a mathematical biologist at the University of New Mexico, and his colleague Jingyi Gao, a doctoral student at the University of Wisconsin. Like the branches, twigs and leaves of a tree, fractals repeat the same patterns across different scales. Snowflakes, lightning bolts and human blood vessels are also fractal structures, which all show a degree of self-similarity: As you zoom into the details of a fractal, you can see a replica of the whole. 'If you look at a tree, its branches are branching. Then the child branches repeat the figure of the parent branch,' Gao said in a news release. Newberry and Gao chose to study artworks depicting single trees. Their selections, which they said spanned different times and cultures, included 16th century stone window carvings from the Sidi Saiyyed Mosque in India, an 18th century painting called 'Cherry Blossoms' by Japanese artist Matsumura Goshun and two early 20th century works by Dutch painter Piet Mondrian. They also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). They found that the trees depicted in the artworks, even when abstract or stylistic, mostly, but not always, corresponded to branching patterns and scale found in natural trees. 'Any kind of abstraction is a way of trying to get at natural laws, whether it's a mathematical abstraction or an artistic abstraction. There's a lot of different kinds of trees in the world, but this theory shows us (and) gives us some baseline for what we expect a tree to be,' Newberry told CNN. Newberry said he had long been a fan of Mondrian's work and how the artist depicted trees in abstract ways, removing all but the most essential elements but still clearly conveying a tree. It jibed with his own work explaining mathematically how treelike structures in human biology such as veins and arteries and lungs use their physical form to efficiently deliver blood and air. To reach their findings, the researchers successfully came up with a method of assessing branching patterns in trees and generalized it into a simple common formula, according to Fabian Fischer, a researcher at Technical University of Munich in Germany who wasn't involved in Newberry and Gao's study. 'The method is based on ideas that go back to Leonardo da Vinci and have been revisited by biologists multiple times,' Fischer said. 'I found it a highly stimulating read, with an interesting connection between works of art and biology.' Scale of 1 to tree In nature, fractal patterns aren't just aesthetically pleasing, they're also often related to function. For example, branching enables trees to transport fluid, harvest light and maintain mechanical stability. Since a fractal is a geometric shape, mathematicians can calculate its complexity, or fractal dimension — even when it appears in art. 'There are some characteristics of the art that feel like they're aesthetic or subjective, but we can use math to describe it,' Gao said. In their research published in the scientific journal PNAS Nexus on February 11, Gao and Newberry analyzed the variation in the thickness of the tree branches in the artworks they studied. They took into account the number of smaller branches per larger branch and used this information to calculate a number they called the branch diameter scaling exponent. The study found that the trees in the artworks had a branch diameter scaling value broadly matching the 1.5 to 3 range for real trees. Outside those values, the objects depicted weren't easily recognizable as trees. Gao and Newberry were surprised to find the highly stylized Indian mosque carving had a value closer to real trees than the tree in 'Cherry Blossoms,' which they had initially thought was more natural-looking. Though extremely rich in detail, with over 400 individual branches, 'Cherry Blossoms' exhibited a scaling exponent of 1.4, while the pair calculated the Indian carved tree has a value of 2.5. Newberry said that having a more realistic branch diameter scaling factor may have enabled artists to take more creative risks yet still have the object recognizable as a tree. 'As you abstract away details and still want viewers to recognize this as a beautiful tree, then you may have to be closer to reality in some other aspects,' Newberry said. Of course, artists such as Mondrian and Klimt would likely not have been aware of fractals, or the math that underpins them, but perhaps had an innate understanding of the subtle proportions all trees share, according to the researchers. However, Fischer noted that the study was exploratory and the range of selected tree species and works of art is small and selective, therefore it's not possible to draw strong conclusions. Fractal pattern impacts The authors studied a series of works by abstract painter Mondrian that depict the same tree but in increasingly less realistic ways. His 1911 work 'De Grijze Boom' ('The Gray Tree') shows a series of black lines against a gray background, but the painting is nonetheless instantly recognizable as a tree, with its branch scaling value in the real tree range at 2.8. 'I don't think he (Mondrian) is even trying to find the essence of trees but as he's pulling things out, this thing that we think is really important in science ends up being one of the last things to go (away) in the art,' Newberry said. 'Clearly, he thinks it's really important, and clearly it's really important to human perception.' However, in Mondrian's 1912 'Bloeiende Appelboom' ('Blooming Apple Tree'), a painting in the same series, the branch diameter scaling is gone, Newberry said, with a value of 5.4. 'Whereas most viewers of Gray Tree immediately perceive a tree, naïve viewers of Blooming Apple Tree see dancers, roots, fish, faces, water, stained glass, leaves, flowers, or nothing representational at all,' the authors noted in the study. The researchers also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). Though the tree's depiction in this artwork is highly stylized, the study's measurements suggest it also fell into the statistical range of a real-life tree. The study authors are not the first to apply math to trees in art. Renaissance polymath Leonardo da Vinci observed tree growth and came up with his own mathematical rule for painting trees. His work on tree physiology inspired scientists and landscape artists alike to study branching patterns, according to the new research. The findings from the study are intriguing because they integrate artistic and scientific approaches to studying trees, said Richard Taylor, a professor of physics at the University of Oregon. 'Although focusing on trees, the article is tackling a much bigger question — why are natural patterns so beautiful — and interdisciplinary collaborations are essential for delivering the answers,' Taylor, who was not involved in the study, said via email. His research has focused on the positive impact of viewing fractal patterns in nature, which he said could reduce stress levels. 'Studies such as this one emphasize the aesthetic power of trees. There is a Japanese tradition known as 'forest bathing,' Taylor added. 'Based on studies such as these, a more appropriate description is 'fractal bathing.' We should soak up the aesthetic qualities of trees — whether this is in nature or in art.'
CNN
14-03-2025
- Science
- CNN
Trees in art, as well as life, often follow simple mathematical rules, study finds
Trees depicted in famous artworks across a range of styles follow the same mathematical rules as their real-life counterparts, scientists have found. The math concept hidden in this tree art — geometric shapes known as fractals — is apparent in branching patterns in nature and may be key to humans' ability to recognize such artwork as trees, according to Mitchell Newberry, a mathematical biologist at the University of New Mexico, and his colleague Jingyi Gao, a doctoral student at the University of Wisconsin. Like the branches, twigs and leaves of a tree, fractals repeat the same patterns across different scales. Snowflakes, lightning bolts and human blood vessels are also fractal structures, which all show a degree of self-similarity: As you zoom into the details of a fractal, you can see a replica of the whole. 'If you look at a tree, its branches are branching. Then the child branches repeat the figure of the parent branch,' Gao said in a news release. Newberry and Gao chose to study artworks depicting single trees. Their selections, which they said spanned different times and cultures, included 16th century stone window carvings from the Sidi Saiyyed Mosque in India, an 18th century painting called 'Cherry Blossoms' by Japanese artist Matsumura Goshun and two early 20th century works by Dutch painter Piet Mondrian. They also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). They found that the trees depicted in the artworks, even when abstract or stylistic, mostly, but not always, corresponded to branching patterns and scale found in natural trees. 'Any kind of abstraction is a way of trying to get at natural laws, whether it's a mathematical abstraction or an artistic abstraction. There's a lot of different kinds of trees in the world, but this theory shows us (and) gives us some baseline for what we expect a tree to be,' Newberry told CNN. Newberry said he had long been a fan of Mondrian's work and how the artist depicted trees in abstract ways, removing all but the most essential elements but still clearly conveying a tree. It jibed with his own work explaining mathematically how treelike structures in human biology such as veins and arteries and lungs use their physical form to efficiently deliver blood and air. To reach their findings, the researchers successfully came up with a method of assessing branching patterns in trees and generalized it into a simple common formula, according to Fabian Fischer, a researcher at Technical University of Munich in Germany who wasn't involved in Newberry and Gao's study. 'The method is based on ideas that go back to Leonardo da Vinci and have been revisited by biologists multiple times,' Fischer said. 'I found it a highly stimulating read, with an interesting connection between works of art and biology.' Scale of 1 to tree In nature, fractal patterns aren't just aesthetically pleasing, they're also often related to function. For example, branching enables trees to transport fluid, harvest light and maintain mechanical stability. Since a fractal is a geometric shape, mathematicians can calculate its complexity, or fractal dimension — even when it appears in art. 'There are some characteristics of the art that feel like they're aesthetic or subjective, but we can use math to describe it,' Gao said. In their research published in the scientific journal PNAS Nexus on February 11, Gao and Newberry analyzed the variation in the thickness of the tree branches in the artworks they studied. They took into account the number of smaller branches per larger branch and used this information to calculate a number they called the branch diameter scaling exponent. The study found that the trees in the artworks had a branch diameter scaling value broadly matching the 1.5 to 3 range for real trees. Outside those values, the objects depicted weren't easily recognizable as trees. Gao and Newberry were surprised to find the highly stylized Indian mosque carving had a value closer to real trees than the tree in 'Cherry Blossoms,' which they had initially thought was more natural-looking. Though extremely rich in detail, with over 400 individual branches, 'Cherry Blossoms' exhibited a scaling exponent of 1.4, while the pair calculated the Indian carved tree has a value of 2.5. Newberry said that having a more realistic branch diameter scaling factor may have enabled artists to take more creative risks yet still have the object recognizable as a tree. 'As you abstract away details and still want viewers to recognize this as a beautiful tree, then you may have to be closer to reality in some other aspects,' Newberry said. Of course, artists such as Mondrian and Klimt would likely not have been aware of fractals, or the math that underpins them, but perhaps had an innate understanding of the subtle proportions all trees share, according to the researchers. However, Fischer noted that the study was exploratory and the range of selected tree species and works of art is small and selective, therefore it's not possible to draw strong conclusions. Fractal pattern impacts The authors studied a series of works by abstract painter Mondrian that depict the same tree but in increasingly less realistic ways. His 1911 work 'De Grijze Boom' ('The Gray Tree') shows a series of black lines against a gray background, but the painting is nonetheless instantly recognizable as a tree, with its branch scaling value in the real tree range at 2.8. 'I don't think he (Mondrian) is even trying to find the essence of trees but as he's pulling things out, this thing that we think is really important in science ends up being one of the last things to go (away) in the art,' Newberry said. 'Clearly, he thinks it's really important, and clearly it's really important to human perception.' However, in Mondrian's 1912 'Bloeiende Appelboom' ('Blooming Apple Tree'), a painting in the same series, the branch diameter scaling is gone, Newberry said, with a value of 5.4. 'Whereas most viewers of Gray Tree immediately perceive a tree, naïve viewers of Blooming Apple Tree see dancers, roots, fish, faces, water, stained glass, leaves, flowers, or nothing representational at all,' the authors noted in the study. The researchers also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). Though the tree's depiction in this artwork is highly stylized, the study's measurements suggest it also fell into the statistical range of a real-life tree. The study authors are not the first to apply math to trees in art. Renaissance polymath Leonardo da Vinci observed tree growth and came up with his own mathematical rule for painting trees. His work on tree physiology inspired scientists and landscape artists alike to study branching patterns, according to the new research. The findings from the study are intriguing because they integrate artistic and scientific approaches to studying trees, said Richard Taylor, a professor of physics at the University of Oregon. 'Although focusing on trees, the article is tackling a much bigger question — why are natural patterns so beautiful — and interdisciplinary collaborations are essential for delivering the answers,' Taylor, who was not involved in the study, said via email. His research has focused on the positive impact of viewing fractal patterns in nature, which he said could reduce stress levels. 'Studies such as this one emphasize the aesthetic power of trees. There is a Japanese tradition known as 'forest bathing,' Taylor added. 'Based on studies such as these, a more appropriate description is 'fractal bathing.' We should soak up the aesthetic qualities of trees — whether this is in nature or in art.'
Yahoo
14-03-2025
- Science
- Yahoo
Trees in art, as well as life, often follow simple mathematical rules, study finds
Sign up for CNN's Wonder Theory science newsletter. Explore the universe with news on fascinating discoveries, scientific advancements and more. Trees depicted in famous artworks across a range of styles follow the same mathematical rules as their real-life counterparts, scientists have found. The math concept hidden in this tree art — geometric shapes known as fractals — is apparent in branching patterns in nature and may be key to humans' ability to recognize such artwork as trees, according to Mitchell Newberry, a mathematical biologist at the University of New Mexico, and his colleague Jingyi Gao, a doctoral student at the University of Wisconsin. Like the branches, twigs and leaves of a tree, fractals repeat the same patterns across different scales. Snowflakes, lightning bolts and human blood vessels are also fractal structures, which all show a degree of self-similarity: As you zoom into the details of a fractal, you can see a replica of the whole. 'If you look at a tree, its branches are branching. Then the child branches repeat the figure of the parent branch,' Gao said in a news release. Newberry and Gao chose to study artworks depicting single trees. Their selections, which they said spanned different times and cultures, included 16th century stone window carvings from the Sidi Saiyyed Mosque in India, an 18th century painting called 'Cherry Blossoms' by Japanese artist Matsumura Goshun and two early 20th century works by Dutch painter Piet Mondrian. They also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). They found that the trees depicted in the artworks, even when abstract or stylistic, mostly, but not always, corresponded to branching patterns and scale found in natural trees. 'Any kind of abstraction is a way of trying to get at natural laws, whether it's a mathematical abstraction or an artistic abstraction. There's a lot of different kinds of trees in the world, but this theory shows us (and) gives us some baseline for what we expect a tree to be,' Newberry told CNN. Newberry said he had long been a fan of Mondrian's work and how the artist depicted trees in abstract ways, removing all but the most essential elements but still clearly conveying a tree. It jibed with his own work explaining mathematically how treelike structures in human biology such as veins and arteries and lungs use their physical form to efficiently deliver blood and air. To reach their findings, the researchers successfully came up with a method of assessing branching patterns in trees and generalized it into a simple common formula, according to Fabian Fischer, a researcher at Technical University of Munich in Germany who wasn't involved in Newberry and Gao's study. 'The method is based on ideas that go back to Leonardo da Vinci and have been revisited by biologists multiple times,' Fischer said. 'I found it a highly stimulating read, with an interesting connection between works of art and biology.' In nature, fractal patterns aren't just aesthetically pleasing, they're also often related to function. For example, branching enables trees to transport fluid, harvest light and maintain mechanical stability. Since a fractal is a geometric shape, mathematicians can calculate its complexity, or fractal dimension — even when it appears in art. 'There are some characteristics of the art that feel like they're aesthetic or subjective, but we can use math to describe it,' Gao said. In their research published in the scientific journal PNAS Nexus on February 11, Gao and Newberry analyzed the variation in the thickness of the tree branches in the artworks they studied. They took into account the number of smaller branches per larger branch and used this information to calculate a number they called the branch diameter scaling exponent. The study found that the trees in the artworks had a branch diameter scaling value broadly matching the 1.5 to 3 range for real trees. Outside those values, the objects depicted weren't easily recognizable as trees. Gao and Newberry were surprised to find the highly stylized Indian mosque carving had a value closer to real trees than the tree in 'Cherry Blossoms,' which they had initially thought was more natural-looking. Though extremely rich in detail, with over 400 individual branches, 'Cherry Blossoms' exhibited a scaling exponent of 1.4, while the pair calculated the Indian carved tree has a value of 2.5. Newberry said that having a more realistic branch diameter scaling factor may have enabled artists to take more creative risks yet still have the object recognizable as a tree. 'As you abstract away details and still want viewers to recognize this as a beautiful tree, then you may have to be closer to reality in some other aspects,' Newberry said. Of course, artists such as Mondrian and Klimt would likely not have been aware of fractals, or the math that underpins them, but perhaps had an innate understanding of the subtle proportions all trees share, according to the researchers. However, Fischer noted that the study was exploratory and the range of selected tree species and works of art is small and selective, therefore it's not possible to draw strong conclusions. The authors studied a series of works by abstract painter Mondrian that depict the same tree but in increasingly less realistic ways. His 1911 work 'De Grijze Boom' ('The Gray Tree') shows a series of black lines against a gray background, but the painting is nonetheless instantly recognizable as a tree, with its branch scaling value in the real tree range at 2.8. 'I don't think he (Mondrian) is even trying to find the essence of trees but as he's pulling things out, this thing that we think is really important in science ends up being one of the last things to go (away) in the art,' Newberry said. 'Clearly, he thinks it's really important, and clearly it's really important to human perception.' However, in Mondrian's 1912 'Bloeiende Appelboom' ('Blooming Apple Tree'), a painting in the same series, the branch diameter scaling is gone, Newberry said, with a value of 5.4. 'Whereas most viewers of Gray Tree immediately perceive a tree, naïve viewers of Blooming Apple Tree see dancers, roots, fish, faces, water, stained glass, leaves, flowers, or nothing representational at all,' the authors noted in the study. The researchers also examined Gustav Klimt's 1909 painting 'L'Arbre de Vie' ('Tree of Life'). Though the tree's depiction in this artwork is highly stylized, the study's measurements suggest it also fell into the statistical range of a real-life tree. The study authors are not the first to apply math to trees in art. Renaissance polymath Leonardo da Vinci observed tree growth and came up with his own mathematical rule for painting trees. His work on tree physiology inspired scientists and landscape artists alike to study branching patterns, according to the new research. The findings from the study are intriguing because they integrate artistic and scientific approaches to studying trees, said Richard Taylor, a professor of physics at the University of Oregon. 'Although focusing on trees, the article is tackling a much bigger question — why are natural patterns so beautiful — and interdisciplinary collaborations are essential for delivering the answers,' Taylor, who was not involved in the study, said via email. His research has focused on the positive impact of viewing fractal patterns in nature, which he said could reduce stress levels. 'Studies such as this one emphasize the aesthetic power of trees. There is a Japanese tradition known as 'forest bathing,' Taylor added. 'Based on studies such as these, a more appropriate description is 'fractal bathing.' We should soak up the aesthetic qualities of trees — whether this is in nature or in art.'
