A Study of Aesthetics
Using Abstract Artworks
by Kevin Burns, 2014

Over one hundred people participated in a survey, designed to test two theories of aesthetics. One theory proved to be much better than the other, and I used that theory to design some new artwork. A nontechnical summary of the study is provided below. A more detailed manuscript (26 pages) for a scientific audience is in press at Journal of Mathematics and the Arts, and available in preprint here as: Entropy and Optimality in Abstract Art: An Empirical Test of Visual Aesthetics.

What Did the Survey Ask? 
The survey used five pages of abstract artworks. Each page (numbered 1, 2, 3, 4, 5) displayed five panels (labeled a, b, c, d, e) across the page.

Page 1

Page 2

Page 3

Page 4

Page 5

When presented to participants, the five panels across a page were displayed in random order. Each participant was asked to provide two sets of judgments for each page. First, participants were asked to rank the five panels from most to least visually complex. Then, participants were asked to rank the same five panels from most to least aesthetically pleasing.

What Do the Theories Say? 
The survey was designed to test two theories of aesthetics. One theory is dubbed B&B', referring to scientists George Birkoff (B) and Max Bense (B') who developed an influential model of aesthetics based on mathematical principles. The other theory is dubbed EVE', referring to psychological processes of expectation (E), violation (V), and explanation (E'). These processes have been theorized to affect aesthetics and are also modeled using mathematical formulas. The two theories make different predictions about how humans will judge the visual complexity and aesthetic quality of artworks in the survey.

Predictions made by the theories of B&B' and EVE'.

B&B'  EVE'  
Visual Complexity 
Based on number of lines.  Based on number of lines and spacing between lines. 
Aesthetic Quality 
Best at minimal complexity.  Best at intermediate complexity, between minimal and maximal. 

What Do the Data Show? 
A total of 148 people completed all 5 pages of the survey. Each set of rankings ("most to least") was converted to numbers 5, 4, 3, 2, 1, where 5 = "most" and 1 = "least". These rankings were then averaged across all participants, separately for visual complexity and aesthetic quality.

Average Rankings of Visual Complexity 
Page 1 Page 2 Page 3 Page 4 Page 5 

Average Rankings of Aesthetic Quality 
Page 1 Page 2 Page 3 Page 4 Page 5 
To test B&B' and EVE', the mathematical models from each theory were used to compute rankings comparable to the human data. Statistics were used to score the match between theory and data, ranging from 0% (a poor match) to 100% (perfect match). Scores for each page were averaged over the five pages of the survey, and EVE' scored much better than B&B'.

Scores for B&B' and EVE' in predicting human judgments.

B&B'  EVE'  
Visual Complexity 
60%

98% 
Aesthetic Quality 
42%

91% 
An important finding from the survey is that individual preferences for complexity vary widely between people. To see this, each person's rankings on pages 14 were used to compute a number (C) between 1 and 5. This number represents the person's aesthetically optimal level of complexity.

Only one person always preferred the most complex image on a page (C = 5); eleven people always preferred the least complex image on the page (C = 1); and the vast majority of people were somewhere in between. So apparently it is impossible for an artist to design an artwork that everyone will find more aesthetic than other artworks of the same genre. However, the above graph does suggest a sweet spot for visual complexity, between 2 and 4 (on a scale of 15), which will be nearly optimal for a large fraction of people. An interesting finding from the survey concerns the colored panels on page 5. The most complex of these panels (labeled e) was designed to approximate a Mondrian painting (New York City I), by replicating the positions and colors of lines appearing in the original painting.

Page 5

This image (labeled e) was judged to be the least aesthetic of the five panels on page 5. Instead people preferred a simpler design, in which there are many fewer yellow lines.

How Can Science Make Art? 
After the experiment, EVE' was implemented in a computer program to create new images  all near the sweet spot of aesthetics. Using three images composed by the program, I constructed the wall sculpture shown below:

Each panel of this triptych is 3' x 3' and constructed of maple slats 1.5" x 0.75" in thickness. Each panel (left, middle, right) has a metaphorical title (Cleveland, Worcester, Cambridge) and mathematical subtitle (V = 4.6, V = 4.4, V = 4.5) reporting the numerical value of visual complexity (V) computed by EVE'. Below are two more sculptures constructed from images composed by the program. For these sculptures, I painted the inwardfacing surfaces with a nod to Mondrian's palette of primary colors. This gives each bounded area a faint colored glow when the sculpture is hung on a white wall. The first sculpture, made of maple and shown in frontal view, is titled Amsterdam (V = 4.5). The second sculpture, made of red oak and shown in frontal and oblique views, is titled Budapest (V = 4.5).


