Do artists and scientists see the same thing in the shape of trees? As a scientist who studies branching patterns in living things, I’m starting to think so.
Piet Mondrian was an early 20th-century abstract artist and art theorist obsessed with simplicity and essence of form. Even people who have never heard of Mondrian will likely recognize his iconic irregular grids of rectangles.
When I saw Mondrian’s 1911 “Gray Tree,” I immediately recognized something about trees that I had struggled to describe. By removing all but the most essential elements in an abstract painting, Mondrian demonstrated something I was attempting to explain using physics and fractal geometry.
My field of research is mathematical biology. My colleagues and I try to explain how treelike structures such as veins and arteries, lungs and leaves fine-tune their physical form to efficiently deliver blood, air, water and nutrients.
Fundamental research in the biology of branching helps cure cardiovascular diseases and cancer, design materials that can heal themselves and predict how trees will respond to a changing climate. Branching also shows up in ant foraging patterns, slime molds and cities.
From 1890 to 1912, Mondrian painted dozens of trees. He started with full-color, realistic trees in context: trees in a farmyard or a dappled lane. Gradually he removed leaves, depth, color and eventually even branching from his tree paintings. “Gray Tree” uses only curved lines of various thickness superimposed on top of one another at seemingly random angles. Yet the image is unmistakably a tree.
How did Mondrian convey the sense of a tree with so little? The science of trees may offer some clues.
One goal of mathematical biology is to synthesize what scientists know about the vast diversity of living systems – where there seems to be an exception to every rule – into clear, general principles, ideally with few exceptions. One such general principle is that evolution fine-tunes treelike structures in living things to make metabolism and respiration as efficient as possible.
The body carefully controls the thickness of vessels as they branch, because deviation from the most efficient diameter wastes energy and causes disease, such as atherosclerosis.
In many cases, such as human blood vessels, the body exerts much tighter control over diameter than length. So while veins and arteries might take circuitous routes to accommodate the vagaries of organs and anatomy, their diameter usually stays within 10% of the optimum. The same principle appears in tree branches as well.
The precise calibration of branch diameter leads to a hallmark of fractal shapes called scale invariance. A scale invariance is a property that holds true regardless of the size of an object or part of an object you’re looking at. Scale invariance occurs in trees because trunks, limbs and twigs all branch in similar ways and for similar reasons.
The scale invariance in branch diameter dictates how much smaller a limb should be as it branches and how much investment a tree makes in a few thick branches versus many thin ones. Trees have evolved scale invariance to transport water, reach light and resist gravity and wind load as efficiently as possible given physical limits.
This science of trees inspired my colleague and me to measure the scaling of tree branch diameter in art.
Among my favorite images is a carving of a tree from a late-medieval mosque in India. Its exaltation of trees reminds me of Tolkien’s Tree of Gondor and the human capacity to appreciate the simple beauty of living things.
But I also find mathematical inspiration in the Islamic Golden Age, a time when art, architecture, math and physics thrived. Medieval Islamic architects even decorated buildings with infinitely nonrepeating tiling patterns that were not understood by Western mathematics until the 20th century.
The stylized tree carvings of the Sidi Saiyyed mosque also follow the precise system of proportions dictated by the scale invariance of real trees. This level of precision of branch diameter takes an attentive eye and a careful plan – much better than I could freehand.
Indeed, wherever our team looked at trees in great artwork, such as Klimt’s “Tree of Life” or Matsumura Goshun’s “Cherry Blossoms,” we also found precise scale invariance in the diameter of branches.
“Grey Tree” also realistically captures the natural variation in branch diameters, even when the painting gives the viewer little else to go on. Without realistic scaling, would this painting even be a tree?
As if to prove the point, Mondrian made a subsequent painting the following year, also with a gray background, curved lines and the same overall composition and dimensions. Even the position of some of the lines are the same.
But, in “Blooming Apple Tree” (1912), all the lines are the same thickness. The scaling is gone, and with it, the tree. Before reading the title, most viewers would not guess that this is a painting of a tree. Yet Mondrian’s sketches reveal that “Blooming Apple Tree” and “Gray Tree” are the very same tree.
The two paintings contain few elements that might signal a tree – a concentration of lines near the center, lines that could be branches or a central trunk and lines that could indicate the ground or a horizon.
Yet only “Gray Tree” has scale-invariant branch diameters. When Mondrian removes the scale invariance in “Blooming Apple Tree,” viewers just as easily see fish, scales, dancers, water or simply nonrepresentational shapes, whereas the tree in “Gray Tree” is unmistakable.
Mondrian’s tree paintings and scientific theory highlight the importance of the thickness of tree branches. Consilience is when different lines of evidence and reasoning reach the same conclusions. Art and math both explore abstract descriptions of the world, and so seeing great art and science pick out the same essential features of trees is satisfying beyond what art or science could accomplish alone.
Just as great literature such as “The Overstory” and “The Botany of Desire” show us how trees influence our lives in ways we often don’t notice, the art and science of trees show how humans are finely attuned to what’s important to trees. I think this resonance is one reason people find fractals and natural landscapes so pleasing and reassuring.
All these lines of thinking give us new ways to appreciate trees.
This article is republished from The Conversation, a nonprofit, independent news organization bringing you facts and trustworthy analysis to help you make sense of our complex world. It was written by: Mitchell Newberry, University of Michigan
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Mitchell Newberry has published research on tree branching supported by University of Michigan and University of New Mexico. He volunteers with Cool It Burque, a tree-planting group in Albuquerque, NM.
