Much has been written about Piet Mondrian's journey into abstraction, so rather than rehash what has already been written, we decided to quantify abstraction across Mondrian's career as an artist.
Thanks to Artnome’s Digital Collections Analyst, Kaesha Freyaldenhoven, the complete works of Piet Mondrian are available in our public database. After carefully examining each individual work throughout the process of adding images to the database, we both remarked that seeing Mondrian’s work in context has radically altered the manner in which we conceptualize Mondrian as an artist. His evolution into abstraction, through paintings and drawings, is incredible - watching this slow stylistic transition encouraged us to ask ourselves: how do we define an artwork as “abstract”?
What is actually happening to Mondrian's paintings over the course of his life as an artist?
With Mondrian, most people think of the simplified squares painted in vibrant primary colors with lots of intersecting black lines forming right angles.
Piet Mondrian
Composition II in Red, Blue, and Yellow, 1930
Oil on Canvas
86 x 66 cm
Abstraction Score: 0.2819313946
Because of the deceptive simplicity of abstract art, we often hear, "My five year old could make that." This frustration leads people to ask, "How can three colored squares with a few black lines on a canvas become famous? Or worse, a single white diamond shape canvas with two simple black lines?”
Piet Mondrian
Lozenge Composition with Two Lines, 1931
Oil Painting on Canvas
80 x 80 cm
Abstraction Score: 0.1000119845
What many may not understand is that prior to creating abstract paintings, Mondrian began his career as an incredibly talented realist painter. Works created from the 1880s to the early 1900s typically depict landscapes and pastoral settings of his native country featuring rivers, trees, and windmills in a naturalistic style.
Piet Mondrian
Farmstead and Irrigation Ditch with Prow of Rowboat, 1898
Oil on Canvas mounted on Panel
Abstraction Score: 0.4933406639
In the later 1900s and 1910s, Mondrian paints similar subject matter; however, he utilizes diverse stylistic techniques with vivid color palettes.
Piet Mondrian
Evening; Red Tree, 1908-1910
Oil on Canvas
70 cm × 99 cm
Abstraction Score: 0.4704731246
His break in representational painting comes during the late 1910s and early 1920s, in which he shifts in both subject matter and color choices.
Piet Mondrian
Composite 10 in Zwart Wit (Composition 10 in Black and White), 1915
Oil on Canvas
105.1 x 114.3 cm
Abstraction Score:0.3968693713
Piet Mondrian
No. VI /COMPOSITION No.II, 1920
Oil on Canvas
100.5 x 101 cm
Abstraction Score: 0.2121607466
Only when you look across his complete body of work, temporally, can you fully appreciate how he carried his draftsmanship across his entire career in his spiritual quest towards perfect balance and harmony. He was famously quoted as saying:
"To approach the spiritual in art, one will make as little use as possible of reality, because reality is opposed to the spiritual."
But how does one measure abstraction in the work of Mondrian? We were/are not sure it is really possible, but thought of it as an interesting exercise. This task was a bit outside our skill set, so we reached out to Artnome friend Alexander Koch, a postdoctoral researcher at Maastricht University, where he is studying bioinformatics, to provide us with some help.
As a preface, we are thinking of this as a work in progress. I know we have thousands of brilliant readers and we are hoping that folks will want to help think through what quantification of abstraction should look like.
While not sufficient for measuring all abstraction, we felt like simplicity may be a reasonable surrogate for measuring abstraction in the work of Mondrian. By simplicity, we mean the reduction of the color palette and the presence of fewer and fewer lines. Alexander was able to capture these trends by creating a complexity score.
According to Alexander, our complexity score is calculated as follows:
complexity_score = (color_score + variance_score + edge_score)/3
In Alexander's words:
"The color_score is simply the number of colors (RGB values) in an image. The idea is that more colors = more complex image.
"The variance_score is the average of the per-row variance of the grayscale values of all pixels in an image (so per row of pixels, the variance is calculated and then the average is calculated of all these variances). The idea is that higher variance = more complex image.
"The edge_score represents the number of contours that are detected in an image and should give an idea of the number of “hard” edges there are in an image. The idea is that more edges = more complex image.
"These three values are then normalized to values between 0 and 1 (by dividing by the maximal value) and averaged."
Alexander created the excellent chart below. In it we see a sort of dip in complexity when Mondriaan shifted away from the more traditional paintings to his better-known abstract work. As a bonus you can click here or on the image below to access a version that allows you to interact by clicking the image to further explore Mondrian's journey.
We did notice that we ran into some issues with image quality. There were some obvious outliers where less complex/abstract artworks ranked high as a result of grainy reproductions.
Obviously this is not a perfect method for quantifying abstraction. In addition to the variance in image quality, simplicity is just not an ideal surrogate for measuring abstraction. While it works reasonably well for Mondrian, artists like Jackson Pollock actually increased the visual complexity of their work as they become more abstract.
Jackson Pollock
Landscape With White Horse, c. 1934-1938
Oil on Canvas
24 x 30 in.
Jackson Pollok
No. 5, 1948
Oil on Fiberboard
8 × 4 ft
For part two in our series on “Quantifying Abstraction in Art,” we will look at using machine learning tools like Clarifai to train a model on artworks that are realistic and then artworks that are abstract. Our hope is that this may improve upon our Mondrian results, but more importantly, it may be able to account for artists like Pollock, as well.
Have ideas on how we should approach this? We are always open to new ideas and working with people interested in helping out. You can reach me at jason@artnome.com.