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.
‘Tableau I’ by Piet Mondrian, 1921.
Kunstmuseum Den Haag
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.
Grey Tree by Piet Mondrian, 1911.
Kunstmuseum Den Haag
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.
The treeless tree
‘Polder Landscape with Silhouetted Young Tree’ by Piet Mondrian, 1900-1901.
Wikimedia Commons
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.
The science of branching
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…
