Chapter III
The Science behind the Visual Equilibrium

Assumptions:

A painting is a closed set of distinct elements, which exist in relatively homogenous sections and are thus distinguishable from their immediate surroundings.

The number of distinct elements which can become a part of a composition is unlimited.

The only type of classification common to all elements is the level of dissimilarity between them.

The only type of transformation applicable to all elements is a change in the relationship of similarity between them. 

Theses:

A state of perfect visual harmony exists, such that any perceptible change leads to a lower evaluation of the aesthetic value of the whole.

Any transformation that impacts the similarity between all elements of a composition should have only one direction: towards increasing the dissimilarity between them. The opposite leads, ad extremum, to a completely uniform painting. The process of increasing dissimilarity between elements is limitless; thus, it is necessary to introduce constraint. 

The artist determines the limit of dissimilarity for the whole. (For example, they can create a composition using a limited palette, or determine its visual character in some other way.)

All elements must be contrasted with each other to the same degree so that no area disturbs the equilibrium of the whole with local contrast.

Equally, the contrasts between elements must be set at the maximum level, as only then will they maximally emphasise each other’s features. This maximum is determined by the limit of dissimilarity established for the whole painting. It is formed following the requirement to maximally contrast each element with the sum of the rest. (This sum is always the reference point for every new element introduced. Thus, if a new element contrasts with the sum too much or too little, the artist has two options: adjust this contrast to match those within the sum of existing elements; or adjust the contrasts of the sum of existing elements to match the new element.)

Since any element can only be assessed against its surroundings, i.e. against the entire painting, a completely harmonious painting is one where the level of dissimilarity between any element and the sum of all other elements is set at the same, maximum level.

We can describe any closed set of elements of any size as “Sn” and every element of this set as “e”. Thereby, Sn: = {e1, … en}. Furthermore, we can designate the ratio of contrasts between elements as “C”. Thus the harmony algorithm is as follows:

For any element belonging to a finite set of elements, the contrast (degree of difference in appearance) between this element and the sum of the remaining elements of the set is equal to the maximum contrast value for this set.

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How to test this?
Studying the composition requires introducing changes to paintings. The Composition Matters research group made precise alterations, retaining the structure and style of the original images. The introduced changes were minimal, visible enough to produce a noticeable effect, possible to measure in quantitative research. They involved adding or removing elements, introducing minor alterations in colour or contrast, modifying shapes, or moving objects. Holistic modifications, such as changing the saturation of all colours or the contrast on the entire surface of the painting, were excluded. Marginal transformations left the composition unaltered enough to ensure viewers wouldn’t perceive the modified version as a different painting. It also guaranteed the elimination of  participants’ subjective preferences regarding artistic styles and conventions, allowing them to focus solely on the quality of the composition.

In the next stage, the original and modified versions were presented to participants for assessment. The number of participants in the study with high visual sensitivity was large enough to yield a statistically significant result. 

People have different visual sensitivities, and not everyone is capable of evaluating art or its compositional aspect. Yet being an art critic or art expert is not necessary to perceive harmony. Many people who are not professionally engaged with art have a high degree of visual sensitivity and/or the ability to perceive relationships between elements. Naturally, this capacity doesn’t equate to an ability to distinguish between great and mediocre works. Eye-tracking experiments have defined which eye movements indicate high visual sensitivity when looking at a painting. More on this topic can be found in the following paper: Eye Movement Correlates of Expertise in Visual Arts.