For Bia
A pop psychology myth from the 1960s suggests that we are either “left-brained”, meaning logical, verbal and analytical, or “right-brained”, meaning creative, artistic and emotional. More recent research has found that our thoughts and processes don’t happen in isolation in only one part or side but engage the entire brain holistically. For centuries, art and mathematics have been seen as distinct disciplines—one driven by creativity and emotion, the other by logic and precision. Yet, the beauty of mathematical principles has been an enduring source of inspiration for artists, while mathematics has relied on art to visualize its abstract concepts. While I am competent in creating an Excel spreadsheet, I am no mathematician. However, I can show you some profound ways art has been inspired by the beauty and poetry of mathematics, weaving together patterns, geometry, and the universal quest for harmony. No calculator required.
Art’s Silent PArtner: The Golden Ratio
Perhaps the most famous intersection of art and mathematics is the golden ratio or golden mean. This irrational number, approximately equal to 1.618, has long been associated with proportion, harmony, and balance. For example, if you measure the length and width of a face, the ideal result, or most beautifully perceived will be about 1 ½ times longer than it is wide. This ratio, often represented with a golden ratio spiral, appears in natural phenomena—from galaxies to the arrangement of leaves—and has been intentionally incorporated into art and architecture.
overlaid with golden ratio spiral
The ancient Greeks were among the first to consciously use the golden ratio in their designs, most notably in the Parthenon. In Renaissance art, Leonardo da Vinci employed the golden ratio in his drawings of the human body, as seen in his famous work Vitruvian Man. The composition of “The Last Supper” is also believed to follow this mathematical proportion, giving the painting a pleasing sense of order and balance.
Later, the golden ratio continued to inspire modern artists such as Piet Mondrian, whose abstract compositions of rectangles and lines embody the harmony of geometric precision, and Salvador Dalí, who used the golden rectangle in his masterpiece The Sacrament of the Last Supper. The widespread influence of this mathematical principle has cemented its place in both the history of art and our collective understanding of beauty.
Symmetry and Tessellations: The Art of Repetition
Symmetry is another mathematical principle that has fascinated artists. Its innate sense of balance and harmony is visually compelling, creating order within chaos. For mathematicians, symmetry plays a key role in fields like algebra and physics, but for artists, symmetry serves as a tool for composition and structure.
One of the most prominent artists who blended symmetry with artistic expression was M.C. Escher. Known for his mind-bending lithographs and woodcuts, Escher’s work was deeply influenced by tessellations—a mathematical technique of dividing the plane into a repeating pattern without gaps or overlaps. Escher’s fascination with non-Euclidean geometry allowed him to create visual paradoxes, where the viewer is tricked into seeing endless cycles of motion, transformation, and inversion. His intricate tessellations of interlocking animals, birds, and fish are both visually captivating and mathematically profound.
Escher’s work challenges the viewer’s perception of space, reflecting deeper mathematical concepts like infinity and topology. His famous print Relativity shows multiple perspectives coexisting in the same space, a visual representation of mathematical principles of relativity and dimension.
Fractals: The Infinite Beauty of Self-Similarity
Fractals represent another mathematical principle that has made a significant impact on contemporary art. A fractal is a complex pattern that exhibits self-similarity at every scale—no matter how much you zoom in, you will continue to see the same pattern. These shapes often occur in nature, visible in the branching of trees, the structure of snowflakes, and the coastlines of continents.
In the 20th century, mathematician Benoît B. Mandelbrot formalized the study of fractals, introducing what is now known as the Mandelbrot set—a stunningly intricate shape that is infinitely complex. Artists soon became fascinated with the aesthetic qualities of fractals, incorporating them into everything from digital art to architecture.
The fractal structure’s infinite complexity and beauty serve as a metaphor for the natural world’s organic chaos and order, highlighting how mathematical principles govern even the most intricate elements of nature. Artists have used fractals to explore ideas of scale, infinity, and complexity, often applying them to generative art, where mathematical algorithms are used to create intricate visual patterns.
Perspective: The Mathematics of Space and Depth
The mathematical understanding of perspective has been instrumental in transforming the way artists represent three-dimensional space on a two-dimensional surface. Before the Renaissance, most artwork lacked the depth and realism we take for granted today. It wasn’t until artists like Filippo Brunelleschi and Leon Battista Alberti developed the mathematical principles of linear perspective that artists could accurately depict space.
By using vanishing points and the rules of geometry, Renaissance artists like Leonardo da Vinci and Raphael were able to create stunningly realistic depictions of the world. The use of perspective transformed painting into a science of space and vision, allowing artists to guide the viewer’s eye and create depth in their compositions.
The Emergence of Algorithmic Art
In the 21st century, the relationship between art and mathematics has taken a new form through algorithmic art—a genre that uses mathematical algorithms and computational processes to generate artworks. Artists today often employ algorithms to create intricate designs, soundscapes, and visual patterns that would be impossible by hand.
Generative art, one of the most popular forms of algorithmic art, relies on rules-based systems to produce variations of a piece. By tweaking parameters within the mathematical framework, artists can generate infinite variations of patterns, mimicking the infinite possibilities found in nature.
The work of artists like John Maeda and Casey Reas explores the boundaries between human creativity and machine-generated design, blurring the lines between mathematics, code, and art. As technology evolves, the possibilities for algorithmic art continue to expand, offering new ways to explore the beauty of mathematics through the lens of artistic expression.
The Infinite Dance of Art and Mathematics
Art and mathematics may seem worlds apart, but they share a profound connection. Both seek to explore and express the world’s underlying patterns and truths. From the golden ratio to fractals, tessellations to algorithms, the mathematical principles that govern nature have inspired artists to create works that resonate with viewers on a deeper, almost subconscious level.
In many ways, mathematics is the silent architect of art’s beauty, providing structure, harmony, and infinite possibilities. As artists continue to explore new technologies and mathematical concepts, the interplay between these two fields will continue to break down the concept of “right-brain, left-brain”, offering ever more intricate and breathtaking ways to experience the world around us.
Have you ever considered art a mathematic equation? Are you excited or nervous about the evolution of math and art? Leave a comment below!
