Dissecting landscape art history with information theory

Digital scans of landscape paintings were collected from two major online sources: WikiArt (WA) (13) and the Web Gallery of Art (WGA) (14). WA landscape paintings were collected in October 2018 with a total of 12,431 paintings by 1,071 artists assigned to 61 nationalities. WGA data were collected in May 2016 with a total of 3,610 paintings by 816 artists assigned to 20 nationalities. We note that both websites continuously update the dataset, so a larger volume of landscape paintings is available on the date of publication of this research.

While the overall number of paintings from WGA is relatively smaller than from WA, the WGA dataset has a larger volume of paintings produced before 1800 CE. Therefore, we utilize both datasets in a complementary way. We carefully constructed a unified dataset by filtering out the duplicate paintings from both datasets. During the data preprocessing procedure, we also manually removed unsuitable borders and photo backgrounds from the entire digital reproductions in painting dataset. The final dataset includes 14,912 paintings by 1,476 painters from 61 nationalities (Fig. 1A) (SI Appendix, section I has a detailed description and the data curation process). To build a consistent nationality standard, the nationality of WGA artists was assigned based on Wikipedia’s nationality information. We provide the full list of paintings used in the analysis and corresponding metadata in Dataset S1.

We also collected 5,780 abstract paintings by 175 painters from the WA dataset in a separate auxiliary dataset. The abstract painting dataset includes artworks by abstract painters in the three WA categories: “abstract art,” “postpainterly abstraction,” and “abstract expressionism.” Quantifying this corpus throughout this paper roughly translates to an imaginary art historian summarizing the art history of landscape painting while being exclusively trained on this widely available, broadly used, yet of course also limited selection of paintings. Differences of the intuitions of individual connoisseurs are to be expected. However, we believe the differences may spark the development of better benchmarks than WA and/or WGA.

The informational partitioning algorithm of Rigau et al. (39) generally works with images of any color depth. However, for the main analyses of our study, the matrix elements of images corresponding to pixels in RGB colors have been coarse grained into three-bit color (one bit for each RGB value) for the following two reasons. First, an image represented in high color depth with a large number of bits per color component in each single pixel would look more natural and realistic to human vision. However, because the partitioning algorithm we used in this study treats color “indexical” and not gradual, colors with slight differences are considered completely different colors. Therefore, we chose to quantize or coarse grain the painting images to a minimal representation of the color space. Using this method, we also avoid finite-size effects that appear if the pixel size of an image is not sufficiently larger than the number of distinct colors in the respective color system when calculating the compositional information and partitioning position. To minimize this finite-size effect, we choose the minimum number of colors that can represent an image in RGB color space while still capturing the macroscopic shape within the painting. To validate our results, we also checked other color depths such as eight-bit RGB, gray scale, or different thresholds to create three-bit images arriving at similar and robust results. SI Appendix, section III has detailed explanations on the effect of color depth on the partitioning process and a comparison between results obtained from different color-depth systems.

We apply the image partitioning algorithm of Rigau et al. (39) based on mutual information of color palette and subregions in an image. Each image in the dataset was first converted into a matrix representation whose dimensions correspond to image width and height.

The full image is considered an initial partition, and the algorithm progressively subdivides the image according to the partitions that provide maximum information gain at each step. For a random variable $C$ taken from the set of discrete colors in RGB color space, the color palette information of an image is defined as Shannon entropy $H\left(C\right)$:The probability $P\left(c\right)$ is given by $P\left(c\right)=S_c/S$, where $S_c$ denotes the number of pixels taking color $c$ and $S$ is the size of the image.

Considering a painting process as a mapping from the color set $C$ to the set $R$ composed of a finite number of regions in an image, the conditional entropy $H\left(C|R\right)$ is defined aswhere the joint distribution $P\left(c,r\right)=Pr\left[C=c,R=r\right]$ and the conditional probability $P\left(c|r\right)=Pr\left[C=c|R=r\right]$. The compositional information gained from introducing a set of partition $R$ is provided by the compositional information defined as the mutual information:If the image is decomposed into $n$ regions, $R=r_1,r_2,\dots ,r_n$, the compositional information is given by the generalized Jensen–Shannon divergence (JSD):where ${\pi }_i$ is the size of region $r_i$ normalized by the full size $S$ and the regional Shannon entropy $H\left(C_i,r_i\right)$ for the color set $C_i$ in the region $r_i$ is given by

Therefore, given a partition that dissects an image into two regions, $I\left(C,R\right)$ gained from the partitioning is maximized if the dissected subregions are composed of a completely distinct color to other subregions. On the other hand, if the dissected subregions both have same color frequency distribution with the original image, the partitioning offers no meaningful information [$I\left(C,R\right)=0$].

The procedure to find partitioning positions of an image is as follows. During the first partition process, one should calculate the compositional information gain over all possible partitions in both horizontal and vertical directions on the entire image resulting in $w-1\times h-1$ trials, where $w$ and $h$ are the numbers of pixels of weight and height, respectively, of the image. Then, the algorithm selects a partition that gives the maximum information. From the second partitioning process, the algorithm is repeatedly applied to remaining subblocks, and the subblocks are partitioned with lines that offer maximum information for each step. In principle, the partitioning process can be continued until the image is fully decomposed into regions of homogeneous colors. Because the conventional partitioning process takes considerable time to find partitioning positions for a large dataset, we used the Shin et al. (40) line updating bipartitioning (LUB) algorithm to calculate the mutual information for each partition step for faster calculation (detailed descriptions of the LUB algorithm are described in SI Appendix, section II).

In this study, we focus on the first two partitions of painting images to analyze compositional proportion of a painting. This allows for meaningful interpretation as the first two sections classify the images in relation to the most dominant compositional features of the painting. After an image or a subblock of the image is partitioned into two subregions with ratios $a:b$, we define the compositional proportion $r_c$ of the bipartitioned image asHere, $a$ is the height (width) of the first subregion from the top (left), $b$ is the height (width) of the lower (right) subregion for a horizontally (vertically) partitioned image, and the proportion is normalized to $\left(\mathrm{0,1}\right)$. The closer the $r_c$ is to one, the more the painting is divided at the bottom (right).

In principle, an image can be partitioned repeatedly until the image is fully divided into subblocks of completely homogeneous colors. As illustrated in Fig. 1D, a subblock of an image can be partitioned either vertically or horizontally at any partition proportion $r_c$ in each step. However, we find that early partitions in landscape painting show a distinct characteristic compared with later steps.

First, the partition direction of landscape paintings in the early partition steps is mostly found to be horizontal in direction (Fig. 1E), while there was no directional preference in abstract paintings in the first step (Fig. 1F); 86.8% of landscape paintings were horizontally partitioned at the first partition step with larger compositional information than vertically partitioned cases on average (Fig. 1G). The frequent observation of a dominant horizontal partition is mainly due to the fact that landscape paintings usually include a horizon, where constituting colors begin to vary significantly. After around 10 partition steps, the ratio of landscape paintings that are partitioned in the horizontal direction saturated at the point slightly below 0.5. However, abstract paintings did not show any directional preference in composition over all partition steps including particularly the first step. It is interesting that the ratio of horizontal vs. vertical partitions saturates slightly below 0.5 in both painting genres (Fig. 1 E and F). We speculate that this saturation effect is mainly caused by two reasons. First, more images exist in landscape aspect ratio as opposed to portrait aspect ratio, notwithstanding the genre of landscapes or abstract subjects. This means that simply by chance more should be partitioned in a vertical direction. Another reason, especially for landscape paintings, is that whereas large-scale objects in landscape paintings such as sky, earth, and ocean are horizontally placed, there are typically smaller vertical objects often with edges left and right such as trees, plants, and buildings. Consequently, the frequent existence of vertically oriented objects, particularly in the foreground, could cause more frequent partition in the vertical direction in the later partition steps. We provide more detailed verification regarding the two explanations in SI Appendix, section III.

Landscape painting further exhibits distinct characteristics in the amount of compositional information. The compositional information gained from the first partitions in landscape painting is much larger than that of modern abstract paintings (Fig. 1H). This indicates that the initially partitioned subregions in landscape paintings tend to be composed of more distinct colors than other subregions. In contrast, the abstract paintings have relatively less quantifiable information (Fig. 1H). For example, consider the famous abstract–expressionist paintings of Jackson Pollock (1912 to 1956). Pollock’s drip paintings were painted by pouring and splashing paint onto large canvases rolled out across the floor, resulting in a fractal pattern without larger-scale compositional dissections of the canvas. Since the composing colors are distributed relatively randomly in space, the subregions of Pollock’s drip paintings tend to have similar color distributions in the early partition steps compared with the color distribution of the original image as a whole, resulting in little compositional information with regard to meaningful horizontal or vertical dissection.

The distributions of partition proportion $r_c$ also differ over partition steps and genres. Fig. 1I shows the distribution $r_c$ from different partition steps for the total set of landscape paintings. In the first partition step, the distribution of $r_c$ has a relatively sharp peak indicating that artists have employed certain proportions more than other proportions when composing their paintings. As the number of partition steps grows, the distribution of $r_c$ gets wider and becomes flatter. On the contrary, the partitioning position of abstract paintings follows an almost uniform distribution even from the first partition step, implying no typical structure at the macroscopic scale (Fig. 1I).

In this section, we investigate frequency distributions of the dominant composition and compositional proportion in landscape paintings over the entire period of our dataset. First, as we found that the early partitions are a meaningful characteristic in landscape paintings, we study their composing direction and the joint probability distributions of compositional proportion $r_c$ up to the second partition. Partitioning up to the second partition classifies paintings into one of four groups based on the order of two partition directions: horizontal–horizontal (H–H), horizontal–vertical (H–V), vertical–horizontal (V–H), and vertical–vertical (V–V), where H and V stand for a horizontal partition and a vertical partition, respectively. While abstract paintings have a symmetric directional preference on average, landscape paintings show a strong asymmetry in the partitioning direction (Fig. 2A). The proportion of the H–H-type paintings is significantly higher followed by H–V-, V–H-, and V–V-type paintings: H–H $>$ H–V $>$ V–H $>$ V–V.

However, after we explore the temporal change of the distribution of the partition types, a gradual change in composition selected by landscape painters is observed (Fig. 2B). Since the 1600s, H–V-type composition was the most dominant, but its proportion continued to decrease, while the number of H–H-type works gradually increased. The cross-over is found during the midnineteenth century. On the contrary, the fractions of V–H- and V–V-type compositions were kept stable over time.

In order to check whether the global difference over time is attributed to the influence of dominant nationalities in local time periods, we examined the distribution of the composition types over time for each country. Interestingly, the time-varying nature of the composition in the landscape paintings was also observed among individual nationalities. Fig. 2C shows the distribution of composition types of the dominant nationalities over five time periods, where each time bin was set to include the same number of paintings. Here, we choose the dominant nationalities of each period as those that included more than 30 artworks in each period, but we note that the results were robust for other criteria from 20 to 60. Overall, our results suggest that typical compositions in landscape painting differ significantly based on the partition types and exhibit a gradual temporal evolution while transcending concepts of nationality. This also suggests that most of the difference in the use of composition across nationality is possibly rooted in the global temporal structure of the data, while apparent differences in nationality are simply rooted in changes of localized production and/or art historical selection (SI Appendix, Fig. S3 shows the temporal distribution of the datasets across nationalities).

To explore typical compositional proportion for each of the four pairs of partition direction, we plot the four types of joint distributions of partition ratio $r_c$ accompanied by typical sample paintings found near the peaks of the distributions (Fig. 2 D–G). In the H–H-type paintings, the proportion of first horizontal $r_c$ was largest near the 0.40 position from the top. In the next partition step, the second horizontal $r_c$ is found near the 0.47 position from the top in the lower subregion as shown in the sample painting (Fig. 2D). As such, the H–H-type corresponds to the composition of paintings with three horizontal layers, usually depicting a foreground, a middle ground, and a background, as suitable to represent perspective. H–V- and V–H-type paintings have dominant vertical features in the composition therefore balancing both horizontal and vertical elements. In H–V-type paintings, the first partition was found most frequently around the 0.55 position from the top (Fig. 2E). Therefore, the first division cuts slightly down from the middle. However, unlike in H–H-type paintings, the second vertical split in H–V paintings could occur evenly over wide range of ratios. V–H-type paintings most frequently have a first vertical partition position near 0.5 from the left and a second horizontal partition at 0.6 from the top (Fig. 2F). Finally, V–V-type paintings constitute a distinct symmetric shape in the joint probability distribution indicating that the first and second partition can occur equally on any side (left or right) of the painting (Fig. 2G). Overall, the dissection algorithm captures the dominant dissections in painting composition reasonably well. This is surprising as the algorithm obviously has some limitations, as it cannot capture dominant diagonal elements or curved structures of a painting, whereas a human observer corresponding to a more flexible algorithm would certainly do. Similarly for the sample images in Fig. 2 F and G, our algorithm does not capture the exact center position of the tree trunk, which human experts would perhaps naturally consider as an intuitive position to dissect the image frame. Here, it is important to note that our algorithm strictly splits areas of positions at maximum color difference, not at maximum symmetry. This effect is similar to Voronoi vs. Delaunay tessellation and of course, a possible subject of future research (41).

So far, we have explored characteristics of the first two dominant proportions $r_c$ in our full time-aggregated set of landscape paintings. Then, how has the use of compositional proportion in landscape paintings changed over time? We investigate the change of the distribution of $r_c$ in three different types of art historical concepts: discrete creation date time spans of 20 y, conventional style periods, and the oeuvre of individual artists, all of these as found in the original source datasets (SI Appendix, section I has detailed statistics). While we are aware that all of these concepts of date, style attribution, and authorship are more or less agreed on conventions, often subject to ongoing scholarly discussion, we simply treat them as a priori groupings of paintings. We focus on the great majority of Western landscape paintings that are partitioned in the horizontal direction in the first step (86.8%) from 1500 to 2000 CE and their corresponding dissection ratio $r_c$ in the following analyses to allow for clear and intuitive understanding. Essentially, with exceptions, we are looking at the position of the horizon over time (i.e., the physical horizon between earth and sky) or the most dominant chromatic difference in the associated color gradient.

Fig. 3 exhibits the change of the distribution of $r_c$ measured and encapsulated in three different conceptual categories: 1) discrete creation date time spans (20-y bins from 1500 to 2000 CE), 2) conventional artistic style periods, and 3) the oeuvre of individual artists. We analyze the top 25 and arguably least contested conventional style periods with the largest number of artworks in the dataset for the rest of our study. These conventional style periods compose 92.8% of all artworks in the dataset. Regarding individual oeuvres, we focus on 131 painters, all within the top 10% based on the number of paintings in our dataset, in two groups before and after 1800 CE, resulting in 30 and 101 painters from the two periods, respectively. We introduce this separate selection criterion as the number of recorded paintings by painter largely increases from 1800 CE. Applying a uniform selection criterion across all time would possibly cause a selection bias toward the modern era (SI Appendix, section V has the statistics). In Fig. 3C, we exhibit a random sample of 66 (50%) individual painters from the 131 representative painters further restricted for the purpose of visualization. The distributions in all three conceptual categories are sorted and colored by the median year in each group.

In all three cases, the distributions of $r_c$ are mostly unimodal and varying smoothly over art historical time, indicating that there are characteristically dominant compositional proportions used by landscape artists (equivalent to the peak of the respective distribution), while the distribution gradually changes over time instead of showing a singular or a random preference in peak shift. The change of peaks over time periods in Fig. 3A shows three stages. Initially, in the midsixteenth century, a small $r_c$ around one-third was dominant. However, the peak $r_c$ gradually increased from the late sixteenth century and reached its highest value from 1640 to 1680 CE. This high peak $r_c$ was maintained until the midnineteenth century, when the peak $r_c$ gradually decreased toward near the one-third position until the late nineteenth century. This indicates that in the sixteenth century, the dominant horizontal partitioning position was usually above the middle of the canvas, gradually moving to the lower middle until the late seventeenth century. Artists continued to frequently produce high $r_c$ paintings (low horizon) until the midnineteenth century when the dominant dissection position on the canvas starts to move upward again.

The trend of $r_c$ essentially recapitulates the historiography of landscape painting yet is still surprising as it appears systematic at scale beyond anecdotal examples. The overall small values of $r_c$ in the sixteenth century intuitively fit artists who started to produce “pure” landscape paintings, such as Joachim Patinir in the Netherlands, who produced a style of panoramic landscapes with small figures from a high aerial view point known as “world landscape.” A similar composition was also created by Pieter Bruegel the Elder. The high aerial view with a large portion of ground results in images partitioned by a high horizon. From the seventeenth century, paintings begin to exhibit increasingly high $r_c$. This trend is exemplified by a group of Dutch landscape painters, such as Jan van Goyen (1595 to 1656) and Salomon van Ruysdael (1602 to 1670), as these Dutch painters depicted landscapes where the sky occupies a larger portion of the canvas (e.g., the median $r_c$ for van Goyen’s paintings is 0.69). The trend of high $r_c$ continued up to the early and midnineteenth century, where painters such as John Constable (1776 to 1837), Caspar David Friedrich (1774 to 1840), and William Turner (1775 to 1851) also expressed their mastery with a focus on the sky. From the midnineteenth century, the peak proportion starts to decrease and moves toward the one-third position, implying that the painting is partitioned around the upper third line of the canvas (Fig. 3 A and B). A possible interpretation is that a relatively small number of paintings utilized a large portion of the canvas to depict the sky. We note that the distribution of $r_c$ also becomes broader in the nineteenth century, indicating a more diverse use of compositional proportion.

The midnineteenth and twentieth centuries are commonly assumed to be a period when a diversity of conventional artistic styles flourished, leading to supposedly completely different artistic styles coexisting in parallel. Grouping paintings by these conventional style periods, we can see if the common assumption of stylistic difference can be put into question by measurement (Fig. 3B) (SI Appendix, section I has the percentage of each style period in the dataset). Overall, the trend of the peaks and distributions follows a similar pattern to Fig. 3A. Focusing on the most well-known conventional style periods, we find that baroque painters frequently used large $r_c$ (peak at $r_c\approx 0.57$), while in the rococo and Romantic periods, we commonly find a proportion near one-half (peaks at $r_c\approx 0.54$ and $r_c\approx 0.52$, respectively). In realism, impressionism, and later styles, the dominant proportion then started to decline, reaching a position near one-third in the upper half of the canvas. Postimpressionism and expressionism are examples with a peak $r_c$ close to one-third (Fig. 3B). An interesting observation is that despite the well-known high diversity in painting styles and topics in the modern era, the distributions of $r_c$ of various artistic styles in the twentieth century are similar with the peak $r_c$ located near the one-third position from the top. In other words, landscapes in different twentieth century “styles” or “isms” seem to share a common mode of construction. We further study the distributions of $r_c$ of individual painters. Fig. 3C shows the distributions of compositional proportions for the random 50% sample of individual artists with the largest numbers of paintings in our dataset. While naturally subject to larger fluctuations due to the smaller number of images per artist, the peaks for individual artists still demonstrate a similar trend in $r_c$. Consequently, we are able to investigate temporal clusters of individuals in detail based on similar use of compositional proportions in the following section.

The fact that each compositional proportion distribution for time periods, artists, and style concepts has distinguishing characteristics naturally suggests consideration of clustering between the distributions to characterize separation and confusion. Which artists and styles are similarly characterized with regard to their typical $r_c$ distribution? Which are far apart from each other? Can we find communities of artists and styles sharing a similar use of dominant compositional proportion? To answer these questions, we compare the distributions of $r_c$ within and between individual artist oeuvres and styles periods. Doing so, we effectively treat both “artists” and “style attributions” as groups of artworks, much like they may form latently in the mind of an art historian or a trained neural network. We define a proportion similarity measure $J$ between two distributions of $r_c$ between $P_i$ and $P_j$ using an information-theoretic distance, the JSD:where $H$ is the Shannon entropy with base 2 and the proportion similarity $J$ is bounded between zero and one.

We investigate how individual artists cross-correlate with multiple styles in terms of horizon choice. We first create a bipartite or two-mode network composed of landscape artist oeuvres and conventional style periods, respectively, to detect groups of artists and style periods with similar habits of composition in paintings. We measure the distributions of $r_c$ of the same 131 representative individual painters and 25 conventional style periods as used in the previous subsection. Then, we set the weight of links between pairs of artists and styles by the proportion similarity between their $r_c$ distributions. From the originally fully connected bipartite weighted network, we then compute a significance criterion for each link following the procedure described in ref. 42. We only keep significant links at the level of $\alpha =0.366$, which maximizes $N_b/N_0-L_b/L_0$, where $N_b$ ($L_b$) and $N_0$ ($L_0$) are the numbers of nodes (links) in the filtered network and the original network, respectively. Then, we apply the Louvain community detection algorithm (43, 44) on the filtered network, which is a fast hierarchical community detection algorithm widely used in network science, to find hidden community structure.

In the final similarity matrix in Fig. 4A, we observe that the compositional similarity network has a clear community structure with three groups of artists and style periods based on their distribution of using particular compositional proportion. Within each community, the link density is high, and the weights of links tend to be much larger than between communities off the diagonal. Each community has two distinguishing features from the others (Fig. 4B). The first feature is the shape of the aggregated $r_c$ distribution of paintings in each community. Fig. 4B shows the distribution of $r_c$ and production year of paintings by all artists in each community. The distribution of dissection proportion $r_c$ in each community has clear difference from the others. Community 1 has the largest peak dissection position (peak $r_c=0.531$), and the distribution is sharper with smaller SD ($\sigma$ = 0.15). Community 3 has smaller peak position (peak $r_c$ = 0.303), and the distribution is much wider ($\sigma =0.21$). Community 2 has intermediate characteristics between communities 1 and 3 (peak $r_c=0.393$, $\sigma =0.17$). Another remarkable feature is that without including any explicit metadata regarding information on the activity time of artists or their stylistic classification, the artists and styles are meaningfully grouped in terms of time period (Fig. 4 A and B). At a minimum, this means the metadata are coherent with the visual features of the images, pointing to a coherent classification by individual qualitative art historians. Of course, critical eyes may surmise that the emerging metanarrative seems almost too coherent to be true. This would mean the classification is coherent yet leaves out everything that does not fit into the all to smooth story of Western art.

Looking into details, community 1 in Fig. 4A is characterized by high $r_c$ paintings and contains most of the artists before 1850 CE. Conventional styles up to the midnineteenth centuries in the dataset fall into this group. Community 2 exhibits a peak at $r_c=0.393$, which is above the middle of the canvas and contains many artists who worked during the late nineteenth century and some in the early twentieth century. Realism, impressionism, and related painters characterize this group in an exemplary way. As we have seen in Fig. 3, from the periods of realism and impressionism onward, the dominant partitioning proportion began to decrease. As such, this period bridges the classically preferred composition to the newly preferred composition in the modern period. This result is in line with the established studies that realism and impressionism served as the transition toward the modern era. Lastly, artists in community 3 show a distribution of $r_c$ with the smallest modal value among the three groups (Fig. 4B) with a less pronounced peak $r_c$ found at the near–one-third position ($r_c=0.303$). Looking at temporal distribution, the paintings in community 3 are mainly concentrated in the early twentieth century, with some in the late nineteenth century. The characteristic shape of the $r_c$ distribution is broader than in the other two communities, representing a more diversified use of proportional dissection. However, contrary to the common notion that the styles or isms of the modern era are distinct stylistic expressions, their distributions of compositional proportions are similar and clustered into a same group: the peak $r_c$ of aggregated paintings (Fig. 4B, third column) and each style’s peaks (Fig. 3B) were all found near $r_c=1/3$. In other words, “anything goes” not only across modern isms but also, within each single ism, while “anything” is bounded with a bias to $r_c=1/3$. As such, it is not individual isms that correspond to conventional style periods such as renaissance or baroque. Instead, one could argue that the sum of isms is the actual style period of isms, which all behave the same with respect to proportional dissection while differing in more limited ways only, particularly in their textual phenotype. One could say all isms share the same generating function regarding the dissection of landscapes.

We also investigate the proportion similarity matrices between all pairs of artists and conventional style periods (Fig. 4 C and D). To compare the clustering of artists and style periods within each concept with the joint artist–style clusters, we newly grouped individual artists and style periods into three communities using the same community detection algorithm. Clustering of artists and styles (Fig. 4 C and D, respectively) correlates meaningfully with the artist–style clusters, again exhibiting clear clustering structure in time. At the same time, the pure artist and pure style clusters deviate from the joint artist–style clusters (Fig. 4A) in detail and consequently, also from the respective one-mode projections (SI Appendix, Figs. S19 and S20), which means we can identify exceptions to the respective superera mainstream in individual artist oeuvres and style concepts.

This effect is in line with Fig. 3 B and C, where the systematic evolution of $r_c$ appears more clear for conventional style periods than for individual artists due to the existing heterogeneity on the level of individual. This result points to the fact that the grand narrative of Western art history, as expressed in the coarse-grained conventional style periods, is too smooth and somewhat artificial, failing to capture the rich nonlinearity of art production throughout time on an individual level. Put in other words, our quantification indicates that a proper grand narrative of art history requires a multiplicity of perspectives, both qualitative and quantitative, as a great amount of nonlinear detail gets lost in an overly conventional mainstream narrative.