Wednesday, May 2, 2018

Simplicity, complexity, and snowflakes

Nikolai Timkov "A Bright Day" 1963

“Science is nothing other than the search to discover unity in the wild variety of nature, or more exactly, in the variety of our experience. Poetry, painting, the arts are the same search for unity in variety.” J. Bronowski (1908-1974) was a British mathematician, historian of science, theatre author, poet and inventor. He was also the presenter and writer of the 1973 BBC television documentary series and accompanying book The Ascent of Man.


“The measure of aesthetic value is in direct proportion to order and in inverse proportion to complexity.” George David Birkhoff (1884-1944) was another prominent mathematician who proposed a theory of measuring beauty in the book Aesthetic Measure.  

Birkhoff defined a typical aesthetic experience as a combination of three successive phases: (1) the act of attention, that increases proportionally to the observed object’s complexity (C); (2) the feeling of value or aesthetic measure (M); and (3) the realization that the object is characterized by a certain harmony or order (0). The mathematical formula he proposed defined the relationship of the three phases.

While the proposal of a formula to measure aesthetics may be interesting to some, most of us would probably just experience an eye-crossing moment of “huh?” But the take-away on this is the recognition of the relationship of simplicity and complexity, or as Bronowski pointed out – the unity in variety. Complexity is responsible for increasing the observer’s attention. Simplicity and the perception of order and pattern trigger a sense of answer or completion – a brief aha moment of “yes, this makes sense”. This is merely recognition of orderliness in a universe that is also dynamic and continually changing. 

Fedor Zakharov
Order and change, unity and variety, and simplicity and complexity are complementary. They co-exist in a continual feedback and response loop. How these elements coexist, and in what kind of proportional relationship, determine how a painting, or any other object we choose to create, looks and feels.





The visual aesthetics of snowflakes


Simplicity and complexity were the focus of researchers at Western Kentucky University who set out to quantify aesthetic experience by asking subjects to rate the perceived beauty of snowflakes and solid objects. Participants were presented with a set of ten snowflake silhouettes created from photographs of natural snowflakes that varied in complexity and ten randomly-shaped, computer-generated, solid objects that also varied in complexity. The results for the solid objects showed a preference for both the most and least complex objects, while moderately complex objects were rarely selected. The results for the snowflakes, however, were different. The least complex snowflakes were almost never chosen: 91 percent of participants perceived only the complex snowflakes as the most beautiful. 

The infinite variety of snowflakes

We have a tendency to overlook complexity when categorizing and visualizing information. The iconic image of a paper cut-out snowflake is probably the first visual that comes to mind when one mentions the word “snowflake”, but it’s suggested from the WKU study that people respond positively to complexity in natural forms when given a choice. It is also possible people are responding to complexity in conjunction with, not apart from, a sense of perceived order.

Chaos and order are defining features of the natural world. While the basic structure of a snowflake is determined by the scientific process of crystallization and all snowflakes start out in the same way, the actual formation of a snowflake is dependent on more chaotic atmospheric conditions, such as temperature and humidity. A snowflake’s growth is one of both order and chaos. No two falling snowflakes will meet precisely the same circumstances on their way to the ground; even the appearance of symmetry will be an illusion since the microscopic space of the growing crystal will contain subtle differences.

The process of snowflake formation is a perfect example of simplicity and complexity. It is also a perfect example of the dynamic forces of chaos and symmetry that create form in both nature and art.

Photo of natural snowflakes by Kenneth G. Libbrecht

Next winter, if you are fortunate enough to enjoy a bright, sunlit, snow-covered landscape, remember you are looking at all the colors of the rainbow. When sunlight hits snow, its full spectrum of wavelengths is almost entirely reflected back at us – every spectral color – red, orange, yellow, green, blue, and violet.

Notes for painters:
  • Simplicity and complexity coexist, just as light and shadow, and warmer and cooler colors coexist. This is all part of the variety in unity. A memorable painting is one in which all the pieces combine to form something new, one in which the whole is greater than the sum of its parts.
  • Complexity does not necessarily mean more detail. Texture, color pattern, and variety in shapes and edges all contribute to the perception of complexity.
  • Learning to see complexity is a form of understanding; editing the information one sees is the key to a strong and insightful painting.



Sunday, March 4, 2018

Breaking the "rules" and changing the parameters of perception

“When the great English painter Sir Joshua Reynolds explained to his students in the Royal Academy that blue should not be put into the foreground of paintings but should be reserved for the distant backgrounds . . . his rival Gainsborough – so the story goes – wanted to prove that such academic rules are usually nonsense. He painted the famous ‘Blue Boy’, whose blue costume, in the central foreground of the picture, stands out triumphantly against the warm brown of the background.”
(E. Gombrich, The Story of Art)

The complexity and endless variety of color information should make any painter wary of rules that limit possibilities. The history of art reveals a pattern of experimentation, innovation, and visual interpretation that form a fascinating time-line of both continuity and change.

We can see millions of colors, far more than we are able to mix with pigments. Also, the range of value (luminance) in a natural scene is almost always far larger than the range of values one can achieve with pigments. According to Margaret Livingstone (Vision and Art), the range of luminance in a room lit by a window or lamp may vary by hundreds of times, and the luminance in an outdoor scene can vary by a factor of a thousand. The range of values available using paint or photographic paper varies, at most, by a factor of twenty.

Artists have dealt with these limitations for centuries. There is not one solution for interpreting a three-dimensional scene on a two-dimensional surface using pigments which can never equal the contrast range or the colors we actually see.  But great artists throughout various periods of art history made one discovery after another that allowed them to interpret and create a convincing picture of the visible world.

The use of oil paint in the fifteenth century led to a greater range of rich colors and smooth gradations of tone.  There was the discovery of linear perspective, atmospheric perspective, and the use of strong tonal contrast known as chiaroscuro. Over the centuries artists refined these techniques and learned to optimize their command of value pattern and luminance to represent depth on a two-dimensional surface.

Value (luminance) determines our perception of depth, three-dimensionality, movement, and spatial organization. Perceiving light is simpler than discriminating what wavelength (color) it is.

Towards the end of the nineteenth century, there was a break with tradition when artists rebelled against the teachings of the academies and what they saw as predictable and uninspired painting. They realized traditional art, with its emphasis on defining objects with careful shading, did not reflect the reality of the scene outside the window. There are harsh contrasts in sunlight, shadows are not uniformly grey, black or brown, and reflections of light and the kind of light affect our perception of color.

These artists, known as Impressionists, set out on a path of discovery - the exploration of light and color. Empowered by the invention of the tin paint tube, they took painting outdoors to create unplanned and spontaneous paintings. Even those who remained studio painters, such as Edgar Degas, shared an interest in scenes that appeared unplanned and spontaneous, as if capturing a split-second glimpse of the world. The advent of photography and exposure to Japanese prints expanded the acceptance of compositions which were once considered unbalanced and incomplete.

The Impressionists, in a radical departure from Renaissance ideals, emphasized light and color, and the transitory nature of visual reality, instead of value and rounded, modeled, solid form. Their use of color changed painting in new and challenging ways, and the change was dramatic. What mattered in painting was not the subject, but the way in which it was translated into color. The old rules of predictable compositions, correct drawing and idealized or picturesque subject matter were set aside for new freedoms of expression in painting. But while the Impressionists were painting a new chapter in art history, some artists found the brushwork and flickering color too messy and incomplete. 


Mont Sainte Victoire by Paul Cezanne, 1895
Cezanne worked to bring solidity, order and design to the Impressionist’s use of light and color without resorting to the academic conventions of drawing and shading.

The Post-Impressionists, such as Cezanne, Seurat, Gauguin, and Van Gogh, brought a desire for order and solid form to the fleeting observations of the Impressionists, but did not want to return to the traditional methods for defining space and modeling form. These artists, while distinctively different from one another, worked to reconcile the pattern and solidity of visual reality with the brilliance and luminosity of color.


The Sower by Vincent Van Gogh, 1888
Van Gogh didn’t hesitate to distort and exaggerate information while using bright color and expressive brushwork.



 Self Portrait by Paul Gauguin, 1890-91
Images that looked flat did not bother Gauguin who sacrificed spatial depth in favor of pattern and color.
The pattern of innovation and change continued as each artist explored various facets of representation. Their work inspired other artists who moved in even different directions. The pointillism of George Seurat inspired Paul Signac’s paintings. Signac’s use of pure color in complementary pairs inspired Henri Matisse. Matisse and fellow painter Andre Derain continued the use of complementary color, but substituted painterly brushwork for the dots used by Signac and Seurat,  All of these painters expanded the dialogue of visual language and changed our ideas about visual interpretation.

The Pine Tree at Saint Tropez by Paul Signac, 1909


Montagne a Collioure by Andre Derain
Woman with the Hat by Henri Matisse,1905
This is an extreme example of Matisse' work during the Fauve period.  He discovered he could use any color as long as the value was accurate. Note the lack of any coherent color pattern. The warmer and cooler colors jump around at random with no reference to the actual light source. The darkest value in the painting is the anchor that holds everything together. Matisse's Self-Portrait-1906 still maintains strong color and brushwork, but has a more coherent, although unusual, color pattern.


Self Portrait by Henri Matisse 1906

Complementary colors are pairs of colors which, when combined, cancel each other out. When placed next to each other, they create strong and brilliant contrast. In the traditional red-yellow-blue color model, the complementary color pairs are red–green, yellow–purple, and blue–orange. The modern color model is cyan-magenta-yellow, and the complementary pairs are red-cyan, blue-yellow, and green-magenta.

Color is a property of light and light is not a random scattering of color. Wavelengths of light that we can see range from the longest (red) to the shortest (violet). The pattern of visible light is red, orange, yellow, green, blue, and violet. The colors merge seamlessly from one to the other. We see these colors because of the receptors in our eyes that are responsive to this narrow range of wavelengths. Objects absorb or reflect particular wavelengths of the visible spectrum. What we see are the wavelengths that are reflected back. 

We rarely perceive pure colors, and the colors we do see depend on the available light source. When the light changes, the number and ratio of wavelengths also change.