Mathematical Innovations in a New Interpretation of Vermeer's Masterpiece

From the Renaissance masters to contemporary artists, the utilization of mathematical concepts has played an imperative role in the creation of lifelike and visually captivating portraits; and thus portraiture, as an art form as a whole. Mathematics serves as both a tool and a foundation for portraiture, facilitating the accurate representation of human anatomy, proportion, and perspective.

Made by: Rishaaya Kakar

Medium Used: Colour Pencils

This artwork is a modern interpretation of Johannes Vermeer's Girl with a Pearl Earring, combining elements from Van Gogh's Sunflowers and Starry Night.

At the forefront of this reinterpretation lies the utilization of fractal geometry, a mathematical framework characterized by self-similar patterns at different scales. Through the application of fractal algorithms, a mesmerizing complexity to the portrait is combined with its intricate details that can be noticed upon closer inspection. The use of Fractal Geometry provides this artwork with a sense of depth and texture; separate from Euclidean geometry, Fractal Geometry addresses the more non-uniform shapes found in nature and thereby provides a systematic method to capture the “roughness” of some objects.

Yet again, the namesake of this blog; The Golden Ratio finds extensive use in this artwork. As we have discussed in older posts, the Golden Ratio is a mathematical concept that has intrigued artists, architects, and mathematicians for centuries. It is approximately equal to 1.618 and is found by dividing a line into two parts so that the longer part divided by the smaller part is equal to the whole length divided by the longer part. When it comes to portraiture, the golden ratio serves as a guiding principle for achieving aesthetically pleasing proportions and compositions. Artists often use it to determine the ideal placement of facial features such as the eyes, nose, mouth, and ears. By dividing the width of the face into sections according to the golden ratio, artists can ensure that these features are positioned in a harmonious and balanced manner. In this artwork specifically, the position of the girl's head and the placement of the earring alligns with the Golden Ratio, creating a sense of balance and harmony in the composition. Additionally, the spiral shape of the earring itself has been compared to the Fibonacci spiral, a mathematical concept from which the Golden Ratio can be derived.

(Upon closer inspection of the Girl's clothing in the image, we can notice the Golden Ratio being used continuously to create a tessellation of the same)

As for the background of this artwork, and the incorporation of Van Gogh's Starry Night to the same, Mathematics has played an intriguing role, particularly in the depiction of light and motion. While Van Gogh himself may not have consciously applied mathematical principles, scientists and mathematicians have found correlations between his paintings and complex natural phenomena like turbulent fluid dynamics. Through digital analysis of his paintings, researchers have observed patterns similar to turbulent flows, indicating that Van Gogh's brushstrokes may unintentionally represent mathematical concepts. This suggests that Van Gogh's unique perception and representation of light and movement might have tapped into complex mathematical phenomena, despite his lack of formal mathematical training or awareness of such connections.

In this artwork, the integration of mathematics is subtle yet profound. With the integration of the aforementioned mathematical concepts, a sense of visual harmony and realism is achieved. Mathematics provides a structured framework for capturing human essence, showcasing the symbiotic relationship between art and mathematics.