The way artists and scientists perceive tree shapes reveals fascinating overlaps.
As a researcher immersed in the branching patterns of living organisms, I’ve noticed these connections come to life in intriguing ways.
Artistic Exploration of Tree Form
Piet Mondrian, an iconic abstract artist from the early 20th century, sought to explore the essence of form and simplicity.
Even if you’re not familiar with his work, his striking abstract grids are hard to miss.
When I first encountered Mondrian’s 1911 painting “Gray Tree,” it sparked a realization.
The way he captured the complexity of trees in an abstract manner mirrored the ways I approach understanding their structures through physics and fractal geometry.
In my field of mathematical biology, my colleagues and I investigate how tree-like formations, such as blood vessels and leaves, have evolved to optimize the transport of essential substances like blood, air, and water.
The implications of our research extend beyond theoretical applications; understanding branching structures could help us tackle cardiovascular diseases, cancer, and even inspire the creation of self-healing materials.
Interestingly, the principles of branching apply across various domains, from the foraging behavior of ants to the layout of urban environments.
Scientific Perspectives on Fractal Structures
Between 1890 and 1912, Mondrian produced a series of tree paintings, starting with realistic interpretations placed within detailed landscapes.
Gradually, he began to strip away color and depth, culminating in works that seemed to deconstruct the entire concept of a tree.
In “Gray Tree,” he employed a collection of curved lines, varying in thickness and arranged at jagged angles, resulting in a distinctly recognizable representation of a tree, despite its simplicity and abstraction.
Mondrian’s minimalist approach allows for a deeper understanding of trees through scientific frameworks.
A key goal in mathematical biology is identifying broader principles that explain the diverse manifestations of life, even amid exceptions.
One significant principle shows how evolution optimizes treelike structures to enhance the efficiency of metabolic processes.
Take, for example, the body’s strict regulation of blood vessel diameter.
Any notable deviation from an ideal width can cause energy loss and lead to health issues, such as atherosclerosis.
This principle becomes especially apparent when considering diameter control over length; while a blood vessel may wind through the body in complex ways, its diameter typically stays within 10% of the optimal measurement—a pattern mirrored in tree branches.
This careful regulation contributes to a defining characteristic of fractal shapes known as scale invariance.
This concept suggests that the same principles apply regardless of the size of the segment being assessed.
In trees, the uniformity of branching patterns at various scales—from trunks to twigs—embodies this scale invariance.
Art’s Reflection of Natural Structures
Thanks to the evolutionary development of scale invariance, trees efficiently transport water, harness light, and endure the forces of gravity and wind.
Inspired by these scientific insights, my colleague and I examined artistic representations of trees, focusing on how scaling manifests in their branch diameters.
A particular piece of art that captivates me is a tree carving from a late-medieval mosque in India.
It celebrates the splendor of trees, echoing literary themes reminiscent of Tolkien’s writings.
The Islamic Golden Age witnessed a remarkable flourishing of artistic and scientific innovations, including the creation of complex, nonrepeating tiling patterns in architecture that remained largely unexplored in Western mathematics until the 20th century.
The stylized tree designs in the Sidi Saiyyed mosque exemplify the use of proportions that reflect the scale invariance found in real trees.
Achieving such precision requires a keen observational skill and meticulous planning—an endeavor that goes beyond my own freehand capabilities.
When examining artworks like Klimt’s “Tree of Life” and Matsumura Goshun’s “Cherry Blossoms,” my colleagues and I consistently found precise scale invariance in the diameters of branches.
Mondrian’s “Gray Tree” brilliantly captures the natural variations in branch thickness while providing minimal contextual clues.
Without this realistic scaling, one might even question whether the painting truly depicts a tree.
In contrast, Mondrian created another piece the following year, titled “Blooming Apple Tree,” which retains similar stylistic elements but lacks the line thickness variability present in “Gray Tree.” This consistent line thickness in “Blooming Apple Tree” diminishes its tree-like semblance, leading the composition to be interpreted as something entirely different.
This comparison emphasizes the importance of branch thickness in representing trees.
The exploration of both art and science often uncovers shared truths about the natural world.
Both disciplines seek abstract understandings, offering a unique satisfaction when their insights coincide, revealing fundamental characteristics of trees.
Much like literary works such as “The Overstory” and “The Botany of Desire,” which celebrate the profound connections we share with trees, the intersection of art and science illuminates our deep-seated bond with the natural world.
This interplay may enhance our appreciation for fractals and natural landscapes, evoking feelings of aesthetic pleasure and tranquility.
Through these varied lenses, we cultivate a richer understanding of the beauty and importance of trees in our lives.
Mitchell Newberry is a research assistant professor of biology at the University of New Mexico.
Source: Fastcompany