"Free will" of painters: choice of color structures

[The work was supported by the Russian Foundation

for Basic Research, grant 02-06-80001a]


Law, say the gardeners, is the sun,

Law is the one

All gardeners obey

To-morrow, yesterday, to-day.



There exist various views on the problem of "free will" of artists. Most of such views concern primarily the phenomenon of socio-cultural dynamics: namely deviations from certain quantitative evolutionary regularities can be used as a measure of artists' "free will" (see, e.g., Golitsyn & Petrov, 1997; Melamid & Petrov, 1998). Meanwhile, "static" regularities can be also used for this purpose, meaning deviations from such regularities inherent in the current functioning of art or structures of oeuvres. Let us consider some of these "static" regularities dealing with the choice of color structures in painting.

1. Theoretical considerations

We should follow the line of one of the models derived in the framework of the information approach (see, e.g., Golitsyn & Petrov, 1995). This model deals with certain limitations inherent in the perception of works of painting, and logical consequences of such limitations result in the following quantitative regularities (Gribkov & Petrov, 1976; Makhmudov & Petrov, 1984; Petrov & Gribkov, 2000):

  1. To provide optimal perception of each oeuvre, an artist should build it containing about 4 - i.e. from three to five - spectral color elements, meaning principal components of 7-color spectrum: red, orange, yellow, green, blue, dark blue, and violet.
  2. As well, to be perceived by the best way, each oeuvre should possess a definite "color-and-light standard", i.e. a certain element (fragment of the depiction) which plays a "tuning fork" for perception of all other color elements used in the given oeuvre. This "standard" is inherent not only in each oeuvre, but it should be common for works of art belonging to a certain "set", for example, those ones which belong to the given national school of painting. As it was shown theoretically, this color-and-light standard should represent the sunlight, and exactly that version (modification) of sunlight, which is typical for the geographic region of the given culture. Therefore, in Northern countries where the dispersed sunlight dominates, this standard should respond to white color. However, in Southern countries the direct sunlight prevails, so the standard should be yellow color. Hence, for instance, Russian painting should use "white" standard, whereas French and Italian painting "yellow" one.
  3. Beside the above standard, there exist certain factors caused by the need for national identification (both of each oeuvre and its author). In order to be ascribed to a definite national school (e.g., Russian or French), most paintings should contain "national color triads" permitting to identify exactly this school: three colors preferred by each national school. Of course, each of such triads should include appropriate national color-and-light standard. As for two other members of the triad, there exist quite definite recommendations which determine their choice: it is desirable that these "additional" colors "compensated" each other, so they are to be placed around the "standard" chosen, the first color being more "warm" than the standard, the second one being more "cold". [In terms of physical optics, one of these members should be shifted towards the short-wavelength part of the spectrum, i.e its violet edge, another to the long-wavelength part, i.e. red edge.] Hence, all members of the triad depend on the color-and-light standard chosen. That is why, for instance, French school of painting chose such national color triad as "yellow, orange, and dark blue" (and the triad of Italian national school was identical), whereas Russian painting chose quite other national triad: "white, red, and green".
  4. The situation of choice of national color triads is sometimes complicated because of "purely cultural" factors (which can compete with the above geographical ones). For instance, the real start of Spanish painting took place against the background of the flourishing French-Italian painting, and afterwards these two schools of painting developed through mutual competition. This circumstance has influenced upon the use of all colors, including the choice of the color-and-light standard. And since "the best places" in the color system were already occupied (by French-Italian school), Spanish painting had to look for a differing use of colors. So it chose its standard not the yellow color, but the white one. Spanish national triad appeared to be "white, red, and black".

Such were the theoretical regularities which formed a basis for our empirical investigation devoted to the quantitative estimation of the "free will" of painters. Evidently, our task should consist in study of painters' personal deviations from these regularities.


2. Empirical data: specific national peculiarities


As soon as the above regularities proceeded from the assumption of optimal perception, they should be valid first of all for undoubtedly excellent oeuvres. That is why four appropriate samples of paintings belonging to above mentioned four national schools, were compiled, using 43 sources: encyclopedias of art, monographs about artists, museum catalogues, etc. In the end, 822 color reproductions relating to easel painting of the XVth - XXth centuries, were involved in the analysis:

  • 311 oeuvres created by 67 French painters;
  • 109 oeuvres created by 33 Italian painters;
  • 106 oeuvres created by 20 Spanish painters;
  • 296 oeuvres created by 47 Russian painters.

Each oeuvre was described by several experts, which used a set of 9 binary parameters evidencing whether each of 7 spectral colors (red, orange, yellow, ...) and 2 non-spectral ones (white and black) is present in the given painting. Then the same experts were asked about "three colors which are the main" in each given oeuvre. So the description of each oeuvre in terms of its "main colors" (using quite analogous 9 binary parameters) was obtained. As a result, each of 822 paintings was "measured" by means of two sets of parameters.

Special computational procedure was used to eliminate possible temporal changes within each sample of national painting. Oeuvres belonging to each national school, were divided into two temporal ranges (an "early" stage of this given national school, and its "late" stage) of approximately equal number of paintings. Then these two subsamples were compared in relation to their distribution over color elements. These distributions appeared constant, possessing only very small differences, which were statistically insignificant. Hence, each national school of painting showed "temporal coloristic stability": the colors used by it, do not depend on time, being determined mainly by its own, "intrinsic" factors.

At last, the specific peculiarities of distributions of paintings (belonging to each national school) over color elements were investigated. It was found that (see Gribkov & Petrov, 1996):

  1. oeuvres of each national school really possess a bell-like distribution (close to Gaussian one) over the number of spectral colors used, with maximum near 4 spectral colors;
  2. French painting and Italian one do not differ from each other on the distribution of all color elements; due to this, it is possible to speak of the "united" French-Italian school of painting;
  3. color-and light standards are statistically different in oeuvres belonging to different national schools of painting; each school prefers to use appropriate elements: yellow color in France and Italy, white color in Russia and Spain - both as "usual" color and "main" one;
  4. national color triads (exactly those ones which were mentioned above) are really inherent in each school of painting examined: these colors are preferred, as well as their triadic combinations.

[Some of the results obtained are summarised in the Appendix; they will be involved in our forthcoming consideration.]

Such were principal regularities concerning the specific features of color distributions inherent in different national schools of painting. Now let us turn to general regularities common for all schools, in order to come to conclusions concerning painters' "free will".

3. "Strength" of regularities, deviations, and painters' choice

Our quantitative estimations of artists' creative "freedom" will be based on the deviations from some strict "obligatory" regularities, i.e. their requirements to the structure of the oeuvres to be created. Of course, the degree of strictness of these requirements can change, in dependence of the nature of each regularity. To be subordinated to a definite regularity, means nothing else than to use an appropriate device. To use or not to use? - Each artist when creating each oeuvre, should answer this question. It does not mean that artists resort to the help of conscious choice, made by means of rational thinking. But in each case, they either use appropriate color construction (i.e. quite definite device), or do not use it, if it were a result of an appropriate choice. How often should artists use these devices?

Information theory permits to answer this question. In principle, here we can deal with two opposite situations.

The first situation responds to the conditions when the given device has no limits to its frequency, i.e. the device simply strengthens the impact of the oeuvre, without any "contra-indications". In this simplest situation the device can be used either seldom, i.e. ad hoc (when it is needed for a specific goal of the given oeuvre) or very often (or maybe always in oeuvres of a certain kind).

The second situation is typical for more or less complicated conditions of functioning of the device, when definite restrictions appear. For instance, on one hand, the device should be consolidated due to its functioning in the system of oeuvres of the kind considered. On the other hand, the device should not distract the perceiver's attention from some other aspects of the oeuvre. The theoretical analysis of such situation (Majoul & Petrov, 2000) showed that in each functioning system of oeuvres two borders should exist for the probability of the device to be met. In other words, the information approach prescribes a certain diapason of admissible probabilities to meet the device. It is desirable that these probabilities were:

  • Higher than the threshold of perception. Otherwise the impact of this device would not be felt, hence the device will not be consolidated in the system (appropriate "invention" can be simply "forgotten"), hence the device will cease its functioning. We know the value of the relative threshold of perception for various kinds of stimuli: for most of them it is about 12 - 15%.
  • Lower than the threshold of realizing. Otherwise the device would be perceived as a deliberate act, and it will be boring. So, the device should be "hidden"; appropriate probability equals to the square root of the threshold of perception, i.e. not more than 35 - 39%.

Such is the diapason of optimal frequency for a certain device in any system of oeuvres, valid for the above typical conditions. Hence, the violations of this regularities can serve as an estimation for the degree of artists' "freedom" of choice. Let us prove these conclusions with our empirical data concerning the frequencies of usage of appropriate color elements (and their combinations) in four national schools of European painting. Empirical data suitable for such proving (obtained while the preliminary stage of the investigation) are summarized in the Appendix.

The only problem concerning such empirical data, is connected with the following obstacle. A painter can use definite color (as well as definite combination of colors) occasionally, i.e. not as a device. Here we mean again not the conscious intention of a painter, but mainly the perception of the color element(s): whether this given element (or this given combination of elements) is perceived as usual, occasional, or it is apprehended as something "specific" (hence, it provides appropriate specific impact in the process of perception of the given oeuvre). Therefore, the main point is the excess over certain "background": occasional probablity to meet this given device, i.e. the given color element or the given combination of color elements.

Firstly let us consider the requirement (a) related to the "recommended" number of spectral color elements used in each oeuvre. In principle, color construction of each painting can consist of 1, 2, 3, ... 7 spectral elements. Assuming equal probabilities for each of seven kinds of such color constructions, we come to the "background" probability to meet a painting built of 3 - 5 color elements, about 3 / 7 = 0.43. In other words, "occasional" color structure containing from 3 to 5 spectral elements, should be met in 43% of all paintings.

Meanwhile, we observe such color structures in 71, 82, 82, and 75% of oeuvres belonging to French, Italian, Spanish, and Russian national schools, respectively (see Appendix, second column). Hence, in French painting the "relative excess" of the usage of this device (in relation to appropriate background value) is (71-43) / 43 = 0.65, i.e. 65% of the background value. For Italian, Spanish, and Russian painting such relative excess equals 91, 91, and 74%, respectively. In all national schools this excess is very high, being indicative of the validity of the first of the above situations, i.e. absence of limits for the frequency.

Turning to the requirement (b) dealing with the presence of color-and-light standard, we should first of all find its background, i.e. the probability to meet occasionally the element which serves as the above standard for this given national school. We know that the main "pretenders" to this role are white and yellow colors. Let us look at their usage as the "main colors" of the painting, because in order to predominate the perception of the entire oeuvre, its color-and-light standard should belong to one of the main colors of this oeuvre.

As soon as in French and Italian painting the above standard responds to color yellow, its "background usage" can be obtained by averaging the frequencies of this color (as one of the "main" colors) in such "non-appropriate" countries as Spain and Russia. This background (calculated on the basis of data presented by Gribkov & Petrov, 1996) equals 0.50. In other words, 50% of Spanish and Russian paintings contain yellow color as one of the "main" elements. And what about real usage of yellow (as one of the "main" colors) in France and Italy? It is close to 55 and 63%, respectively (see Appendix, third column). Hence, the relative excess is 10 and 26%, respectively (see Appendix, third column). Quite similar calculations for white color which should be a standard in Spain and Russia, result in the background value 27%, whereas in reality the percentage of oeuvres with white (as one of the "main" colors) equals 55 and 44%; hence, the relative excess is 104 and 63%, respectively.

At the first glance, these results seem to be rather ill-matched. But it is necessary to remind of some historical circumstances which can shed light on these results. The matter is in that national color-and-light standard plays different roles in national schools in question. In French and Italian painting this standard simply plays a kind of a "tuning fork" for the color construction of each given oeuvre, as well as for the entire system of national painting. That is why such a standard is close to the lower border of the recommended range; in the national system of painting, the usage of such "tuning fork" causes a certain "coloring" of most oeuvres (something like "subtle, imperceptible aroma"). On the contrary, in Spanish and Russian painting the color-and-light standard is used not only as internal "tuning fork" for each oeuvre (and for the entire system of oeuvres), but also as external sign of "national identification". Hence, it should not be "hidden"; moreover, it should be "manifested". That is why its frequency exceeds the threshold of realizing.

Now let us consider such a device © as national color triads. The frequency of its "background" usage can be calculated on the basis of empirical data concerning shares of paintings possessing each separate color element (Gribkov & Petrov, 1996). For instance, appropriate calculations for French painting resulted in the background (i.e. "occasional") value of about 28% - such should be the frequency of combination of colors coinciding with French national triad, if these color elements were combined occasionally. Analogous background for Italian painting is about 25%, for Spanish painting 18%, and for Russian painting 27%. Meanwhile, appropriate real values are 42, 25, 52, and 29%, respectively. Hence, the relative excess is 50, 0, 189, and 7% for France, Italy, Spain, and Russia, respectively.

Here we see again very high diversity of values, which is evidently caused by differences in historical trajectories of the national schools considered. In fact, French painting was leading during all the historical epoch in question, so of course, its oeuvres needed definite national identification, i.e. this device should not be "hidden". Hence, its frequency can exceed the upper limit mentioned (responding to the threshold of perception). On the contrary, it was long ago that Italian painting and French one merged, so Italian painting didn't need specific national identification and showed zero relative excess of its ferquency. Quite opposite situation took place in Spanish painting, which sharply needed national identification (against the background of French-Italian school). That is why we see such a giant excess (189%) of paintings with Spanish national triad. At last, in Russian school the situation was rather original. Though of inclination to national identity, Russian painting was strongly influenced by French-Italian school, and borrowed from it the majority of the devices. (There exist numerous manifestations of such influence, for example, most Russian students of the Academy of Fine Arts were educated either in Italy or France.) So some devices used by Russian painting, are something like a "mixture" of Russian and French style. (For example, many Russian painters used "French palette".) That is why we observe such a small relative excess of the device in question (7%) in Russian painting.

Finally, certain specific features caused by "purely cultural factors" (d), also can be traced in the results reviewed. For instance, the above historical circumstances which accompanied the development of Spanish painting, affected its character: the relative excess of usage of most devices is much higher, than in other national schools, especially in relation to those devices which are not-absolute, culturally conditioned (the national color-and-light standard and the national triad).


4. Concluding  remarks:  painters'  "free  will"


Now it is time to return to our main problem dealing with the artists' "free will". We see rather remarkable panorama of the values of the degree of freedom which are subordinated to quite definite principal regularuty concerning the hierarchy of complexity of devices: the more complicated is the device, the more the freedom of artists' choice (to use this device or not to use it). In fact, the degree of freedom of French artists changes from 29% when choosing the number of spectral elements (i.e. 100% - 71% - see the second column of the Appendix) - to 45% in relation to the presence of national color-and-light standard, and to 58% when deciding about the usage of the national color triad. Quite similar changes (without any exceptions) are observed in Italian, Spanish, and Russian schools of painting.

As well this principal regularuty can be treated as an evidence in favor of a certain hierarchy inherent in the nature of requirements imposed on the creative process. The most "strict" are the so-called "absolute" requirements caused by the very nature of the given kind of art. In the case of painting, these requirements concern the number of spectral colors constituting the color construction of the oeuvre. Here the "room for freedom" is not so great: its average value is 25% (i.e. 100% - 75% - see the last line in Appendix). Not so strict should be the requirements which are "half-absolute", i.e. dealing both with the nature of this kind of art and concrete social (cultural) conditions of its functioning. Exactly such are the requirements concerning the presence of the national color triad. The "freedom" to violate these requirements can be estimated by average value 100 - 52 = 48%. Finally, almost purely "relative" (conventionally-cultural) requirements should allow more "room" for artists' "free choice". In the case of painting, such conditional requirements are represented by usage of national color triad. The avarage value of the freedom not to use this device is about 74%. [The correlation of the above two hierarchies is the topic of a separate investigation.]

The values obtained show rather good agreement with our previous estimations of artists' freedom of creative choice based on dynamic regularities inherent in the evolution of art (Golitsyn & Petrov, 1997; Melamid & Petrov, 1998). As for further development of such investigations, it seems prospective to study the degree of this freedom in the creativity of separate artists, especially eminent ones, in order to connect this freedom with artists' talents.


Golitsyn, G.A., & Petrov, V.M. (1995). Information and Creation: Integrating the "Two Cultures". - Basel; Boston; Berlin: Birkhauser Verlag.

Golitsyn, G.A., & Petrov, V.M. (1997). Styles of creativity: Measurement of changes, their cultural determination, and the problem of "free will" // Aesthetics: Information Approach (Problems of Information Culture, issue No. 5) / Ed. by Yu.S.Zubov and V.M.Petrov. - Moscow: Smysl Publ. P. 123-136.

Gribkov, V.S., & Petrov, V.M. (1976). Semiotic Analysis of Some Aspects of Color Language. - Moscow: Institute of Psychology of the USSR Academy of Sciences; Scientific Council on Cybernetics of the USSR Academy of Sciences (in Russian).

Gribkov, V.S., & Petrov, V.M. (1996). Color elements in national schools of painting: A statistical investigation // Empirical Studies of the Arts, vol. 14, No. 2. P. 165-181.

Majoul, L.A., & Petrov, V.M. (2000). Devices of art (and also of life?): Information approach to the optimal frequency of occurrence // Information Paradigm in the Human Science (Proceedings of the International Symposium) / Ed. by V.M.Petrov and V.P.Ryzhov. - Taganrog: Taganrog State University of Radio Engineering. P. 141-146.

Makhmudov, T.M., & Petrov, V.M. (1984). Methodological Problems of the Aesthetivc Analysis of Art. - Tashkent: Fan (in Russian).

Melamid, L.A., & Petrov, V.M. (1998). "Immanent" periodicity from the informational standpoint: Symmetry in Japanese art revisited // Information Approach in the Empirical Aesthetics (Proceedings of the International Symposium) / Ed. by G.M.Balim, V.M.Petrov, and V.P.Ryzhov. - Taganrog: Taganrog State University of Radio Engineering. P. 251-259.

Petrov, V.M., & Gribkov, V.S. (2000). National characteristics in painting: The psychological basis of color structures // Journal of Russian and East European Psychology, vol. 38, No. 3. P. 64-86.



Appendix. Colors used in four European schools of painting: percentage of oeuvres containing different color elements (appropriate background, i.e. "occasional" values are presented in brackets)



From 3 to 5 spectral elements

National "color-and-light standard" as one of the "main" colors

National color triads


71 (43)

55 (50)

42 (28)


82 (43)

63 (50)

25 (25)


82 (43)

55 (27)

52 (18)


75 (43)

44 (27)

29 (27)

Averaged over four national schools

 75 (43)

 52 (39)

 36 (26)