Is art really a purely subjective phenomenon? Can we decipher a work like Vincent van Gogh’s Sunflowers with math and logic? We can, in fact, by using a formal analysis that examines the artist’s use of color and form.
Objectively then, how did Vincent van Gogh create such an original, beautiful image?
The Three Components of Color
First, let’s examine the mathematical relationships between colors. In order to do this, we must break color down into its three components: hue, saturation, and value (hsv).
Hue is the choice of the color, such as blue. Saturation is the color’s intensity, which contributes to its energy but not its value. Value is the color’s lightness or darkness; the greater the value, the lighter the color, and the greater the energy.
Imagine an airplane moving in space. It can roll, which rotates the plane. It can pitch, which moves the plane up or down. It can also yaw, which changes direction sideways. Roll, pitch, and yaw are like the hue, saturation, and value.
Value and Saturation as Tint, Tone, and Shade
Regarding saturation and value, lighter versions of a color created by adding white are called ‘tints,’ while darker iterations created by mixing black are called ‘shades.’ A desaturated color created by a neutral mixture describes ‘tone.’
Take note that van Gogh’s painting utilizes yellow as its predominant color, though only in tints and shades. “Sunflowers” features very little pure yellow.
Luminosity of Color
If white light has a brightness of 100, blue is the darkest color at 30 and yellow is the lightest color at 98, when translated to grayscale.
Van Gogh relies on yellow in “Sunflowers,” but he balances the image by using tints and shades of this bright color.
Color Wheels and Equations
The three primary colors of the light-based color wheel are red, green, and blue. Primary colors are colors that cannot be created by mixing two other colors. The colors that result from mixing two primary colors are secondary colors. These consist of magenta, yellow, and cyan. Tertiary colors are created by mixing a primary (RGB) and a secondary color (CMY) together, such as red and yellow creating orange.
In the color wheel based in light, the opposite pairs include red and cyan, yellow and blue, and green and magenta.
With pigments, the color wheel is slightly different. Its primary colors are red, yellow, and blue.
Alongside van Gogh’s use of yellow in “Sunflowers,” the artist also features green, orange, and a touch of red and blue. Blue and orange are opposite colors in the color wheel based in pigment, as are red and green. Opposite colors are known to create both balance and contrast in the image because they are symmetrically placed in the color wheel. But why did van Gogh use yellow in conjunction with green and orange, although they are not opposite colors? To find out, we need to examine the other modes of color relationships.
Color harmony is the melodious combination of colors that achieves contrast and/or cohesion in a dynamic manner that is pleasant to the viewer. Color harmony is best understood through the lens of the RYB color wheel in a subtractive system of colors because color harmony can naturally be achieved through mathematical arrangement of colors here.
Complementary (opposite colors)
When we examine these color harmonies, we find that the colors van Gogh employs in his work read so beautifully because they are mathematically equal parts of one another. The balancing components of the color harmony are either equidistant from each other or are placed as equal parts made of single colors or averages of two colors.
Orange, yellow, and green create harmony, even though they are not necessarily opposite colors on the RYB color wheel. They work as color harmonies because they are adjacent colors in this system that deviate to opposite directions in the RGB color wheel involving light (rather than RYB color wheel). In van Gogh’s painting, orange and green are deviations of yellow. From yellow, orange is towards red and green is toward cyan. Red and cyan are opposite colors in the RGB color wheel.
An analogy can be made to speed and acceleration: Speed, which is a change of position, is the color, while the acceleration (or rate of change), is the direction of the color. For example, a green may be green in terms of color, but its direction will be cyan in relation to yellow.
Van Gogh used the principle of opposite colors and the balance of colors within the color wheel to arrive at a cohesive and dynamic image, counterintuitively rife with change and consistency, truths and contradictions. The complementary color scheme of red/green and orange/blue allow the colors to define and contrast each other, while the analogous color scheme of orange, yellow, and green create an internal contrast of yellow to red and yellow to cyan.
“Sunflowers” also has a luminous and spiritual atmosphere. How did van Gogh achieve this ethereal quality?
Change of Hue with Change of Brightness
It is my theory that as colors approach white or black, they become closer to the opposite color. For example, pink, which is a red moving closer to white, contains cyan, the opposite color of red. Crimson, which is a red moving closer to black, contains less red, and negative red also equals cyan.
In fact, it’s possible to see cyan in the tint (pink) of the red relative to red, but it’s difficult to see cyan in the shade (crimson) of the red relative to red. This is because cyan is a much brighter color than red, and while lightening red towards pink can suggest cyan, the opposite of darkening red towards crimson suggests something else. When I look at the crimson, I can actually see blue and dark green, which create cyan. This is more believable because blue and green are darker than cyan and closer to red in terms of brightness.
In van Gogh’s painting, yellow has been lightened into a tint with white. Mixing yellow with white causes yellow to move closer to blue in the color space. Van Gogh also mixed yellow with black to produce Yellow Ochre, which is a shade of yellow. Mixing yellow with black causes yellow to move closer to blue in the color space. Without applying blue directly to yellow, van Gogh pushed the color closer to blue by applying tints and shades of yellow.
Red-orange is the warmest of all colors, and sky blue is the coolest of all colors.
Examining the highlight on the vase in “Sunflowers” emphasizes van Gogh’s familiarity with color. The highlight on the vase is shifted towards cyan, which is close to the brightest point of cool colors. Relative to yellow, the cyan is actually closer to blue, since subtracting yellow from cyan equals cyan plus blue. Relative to cyan, yellow is actually closer to red, since subtracting cyan from yellow equals yellow plus red. Because red is darker and cyan is lighter, both are naturally opposite colors. These subtle color mixtures form high contrast and create a change of energy while maintaining cohesion. Furthermore, cyan is the coolest of colors, and using it is a way to contrast with the rest of the painting, which is warm overall.
Vincent van Gogh’s “Sunflowers” was not a premeditated act of art-making. It was neither planned nor a result of a study. It came about instinctively by the hand of the divinely inspired and genius artist. It is only after the fact that we can subsequently analyze his work logically and mathematically. The sense of wonder and magic about the art and the artist still remains, despite having scrutinized his work using math and logic.
Chun Park (Chunbum Park) was born in Seoul, South Korea in 1991. He came to the United States in 2000 and attended Montgomery Bell Academy for high school. He briefly attended University of Rochester and Bergen Community College from 2009 to 2011. Since 2011, he has aspired to become a practicing artist and studied at various schools, such as the Rhode Island School of Design, the Art Students League of NY, and the School of Visual Arts. He will receive his BFA from SVA in 2020.