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Stochastic Investigations: Squares of Varied Hue, Background and Density

What proportion of human taste is informed by experience and good sense, and how much is arbitrary? How much randomness is acceptable before an artwork is uninteresting?

I began an exploratory project in mid-2021 called “Stochastic Investigations” to shed some light on these questions. My first installment is called “Squares of Varied Hue, Background and Density”. (Exciting, huh?). It’s a series of eight computer-generated designs of colorful rectangular grids. (I currently plan to have them printed on paper or aluminum at around 20x30 or 30x40 inches.)

The premise is simple. I wrote a small software program (in rudimentary Python) to create a rectangular grid, from 11 to 100 units in each direction, pick a background color at random, with no limits or constraints, pick a density from 0 to 100%—the probability that any given square would be colored with a random, unconstrained color different from the background—and automatically generate the pattern on its own[1]. (Future series in this project will have different objectives.)

There were no other constraints. I did not place any other rules or impose any heuristics on the random decisions. To give you an idea of how much randomness is involved in the color selection, a typical computer today can theoretically generate 16.8 million different colors. This is not to say that anyone can see that many colors, nor that computers and printers can successfully print anywhere near that number. A human can probably see around a million colors, and a good printer maybe a thousand or two[2]. I only mention these big, scary numbers to demonstrate that I allowed the software an effectively unlimited ability to select any color at random.

I generated 40 images and selected my favorite eight. I might be accused here of skewing the results by selecting the cream of the crop, but frankly the other thirty-two weren’t that bad. (And hey, give me some credit for not generating 1,000 images and picking the top ten!)I was actually quite surprised at how aesthetically interesting they all were, and how difficult the selection process was. (I initially planned to print 16 but didn’t think there was quite enough thematic variability overall to justify that many.)

Was it because I made the decision to have the computer pick a different background color than white? The first few I generated were done against white, and I didn’t like them so much, so I randomized the background color too. Did that decision influence the experiment? Or was the experiment itself trivial? Is an abstract grid of colorful squares—like an artificial landscape—intrinsically interesting no matter what the colors are?

I’ll let the viewer decide. I feel I achieved a pretty good result, but in future series I can certainly explore more parameters, such as using objects of different shapes and sizes, allowing more randomness in the background, and/or limiting the palettes to only a small handful of colors. (The fewer colors I use, the more important each color is, i.e., the greater chance any one color can mess things up.)

I also puffed out these images to make them conform to a 20x30-inchprint size (which I may enlarge later). Sometimes I used white as an outer filler, sometimes I went with the background color the computer had chosen, and and sometimes I selected a color similar to the background, but not identical. Did I mess up the experiment by doing that? I don’t know. Doesn’t the artist or collector get to chose the mat color when the piece is framed?

No matter what doubts may exist, I think I showed that the selection of palette in an abstract work is not as sensitive to careful consideration as we artists may want to believe. There are of course systems for color selection that experts tell us are profitable ways to assemble palettes—monochromatic, analogous, complimentary, split complementary, triadic, and tetradic—and while I know one must always trust the experts, I’m enough of a heretic to doubt how important these schemes are. Maybe I can study each of those systems in turn as well (with sufficient randomness of course).

Or maybe we are on thinner ground than we are comfortable admitting when we assume that what we see before us is the result of intelligent decision-making—our human prejudice in favor of our own species’ intellectual dominance. Maybe artists and designers should worry less about palettes, and remain more open to chance.

The use of randomness in art goes back a century, starting perhaps with works like Marcel Duchamp’s Three Standard Stoppages (1913-14), where he dropped a meter-long string onto the ground and recorded the shape in which it ended up.

By the middle of the 20th century, the avant garde of all creative endeavors would be motivated to learn what kind of art could be created by limiting the agency of the creator. In 1951, for example, John Cage would compose a piece for solo piano, entitled Music of Changes, using a method he called indeterminacy, in this case inspired by the I Ching (“Book of Changes”). He used the word in response to, and demonstrating a possibly stricter adherence to randomness than the popular 20th century term aleatoric, which implied the incorporation of unpredicted elements (like audience suggestion).

In that same year, Ellsworth Kelly, then living an ocean away,would also experiment in randomness. As Cage arranged Music of Changes, Kelly composed a series of eight collages, called Spectrum Colors Arranged By Chance.

Kelly chose 1-inch squares, and placed them at random on papers about 1 meter square[3]. He selected a color randomly from 18 pre-selected hues, and placed them at random on his pencil grid of 40x40 squares. The squares are described as “cut-and-pasted color-coated paper”. This might mean pre-printed papers(like Color-aid), but one gets the feeling he took inspiration from his fellow Parisian Matisse, who had his assistants hand-paint paper sheets for his beautiful collages—the famous Cut-Outs—made during the same years Kelly was making these collages! Unfortunately I have not yet found an interview where Kelly was willing to discuss the details of this project in any but abstractions and generalities. (Right?)

To determine the placement of each square, Kelly appears to have dropped each square (or something similar) down onto the support papers, with the support papers possibly laid on the floor. I believe this because there is more density of squares in the center of each piece, like you would expect in a normal distribution. For numbers VI, VII, and VIII, however, it appears that he abandoned himself more confidently to chance, going in some sort of order, perhaps something like upper-left to lower-right, and pasted randomly-selected squares as he went along. I believe this because these later collages appear more random, in the mathematico-scientific sense than the earlier ones. I’m on the fence about number V. I suspect he used the same method as he did on I through IV (using pseudo-randomness like dropping the squares onto the paper from a height), but I can’t prove it. Again, I have not yet found a source where Kelly reveals his methods.

In 1953, just after publishing his collages, Kelly would make a painting using the same method, also entitled Spectrum Colors Arranged by Chance, but in this case squares of 4cm in a 38x38 grid for an overall size of 60x60 inches[4].

But let’s end the discussion on Kelly with one last tidbit. I claimed above that he dropped the colored squares onto the paper supports from above. Take a look at his 1950 collage Stigmata: Torn Drawing Rearranged by Chance (pre-dating the above collages by a year). This also looks like he may have jumbled the papers and left them where they lay—whether by dropping them from above, or shuffling them up and leaving them as is—but my engineer’s eye is suspicious of the claim that this is a true random distribution. Truly random distributions are actually kind of ugly. Randomness is by definition uncooperative, after all. My gut tells me that Kelly “curated” this collage to make it look like it was still random, but fiddled the pieces a little bit, to make it remain aesthetically pleasing to the 1950 eye[5].

I do not claim Kelly has misrepresented his use of random chance. I take him at his word, with deep respect for his contribution to this line of inquiry. I admit, however, that I wouldn’t be surprised if it turned out that he had put his finger ever so gently on the scale. His goal was primarily to create great art, after all.

I make this point so strenuously because this is exactly the question my project examines. Stochastic is the word mathematicians use to describe unpredictable processes, the same way Cage used the word indeterminate, Boulez aleatoric, and Kelly chance. How much aesthetic manipulation can I get away with, with as little human curation as possible? How pleasing do we find the result?Maybe unmitigated randomness is destined to remain uninteresting, but I’d like to find the line between openness to chance and the need to tweak. Certain constraints are inevitable—the computer has to produce something, and there needs to be some direction given, however little—but the fewer rulesa priori, the better.

Let these eight images be a first step on a path toward understanding how aesthetics works, how much it depends upon human agency, and how tolerant it is to indeterminacy.

August 2011


[1] I used the HSV model for color generation (Hue-Saturation-Value). Hue can be anything from the color wheel, 0 to 360 degrees, saturation can be from 0 to 100% (from muddy to intense), and value can be the same (from black to full brightness).

[2] A 1975 study suggests a human can see 10 million colors, whereas a 1999 paper suggests 2.3 million. A typical computer probably can’t distinctively display more than 16,000 colors, and many web designers try to keep their palette limited to a small set of 216 anyway (the so-called “web-safe palette”). Even the world-renowned Pantone color system only publishes something like 2,000 colors at the moment.

[3] Actually 39 inches square. The individual papers are a half-meter square each, but four sheets were attached to make one support, except in the first collage, which used only two sheets, thus being 1 meter by a half. I have found no sources that describe the collages this way. When I see “39 inches” I translate this to “1 meter”. (Don’t get me started about 39-and-a-half-foot poles.) And when a “39 inch” artwork is divided into a 40x40 grid, I translate this to “1 inch”. Something deep in my heart tells me that Kelly (or assistants?) did not cut out thousands of paper squares by non-standard measures. Maybe one day I’ll find out for sure.

[4] This mixture of metric and imperial units is fascinating, first inch-delineated squares on centimeter-delineated papers, then the reverse. This can’t be a coincidence. As the popular meme goes:A decision was made here. It would have been the easiest thing in the world to divide up his 60x60 wooden panel into a 40x40 grid, the same as his paper collages, resulting in squares exactly 1.5 inches per side, but he chose instead to use a 38x38 matrix, making the squares just about exactly 4cm square. Something interesting is going on here.

[5] Am I making too much of this? Am I perseverating over irrelevance? I don’t know. If an artist claims to be using chance, which is a highly interesting thing to theorize about, then I think it behooves us to examine exactly what type of chance, and how much. If art helps us understand the human condition, then understanding our response to an artwork may depend upon understanding the creative elements of that work in some detail.

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