WikiArt Visible Artwork Encyclopedia (1), with its 250,000 artworks by 3,000 artists, is a comparatively small on-line database, however supplies loads of numerical information about artists, their artworks and their types. This put up analyses and visualizes the ‘counts’ of WikiArt for 4 well-known artwork types: Romanticism, Realism, Impressionism, Expressionism (Desk 1).

Desk 1. WikiArt numbers of artists and their artworks




whole T

per artist t

whole A




Tnt = A















The variety of artworks per artist n in every fashion differs broadly from 1 to greater than 1000. To interpret the data, the quantity t of artists may be counted in clusters of given numbers of artworks, i.e. cluster 1: 1 to 40 artworks, cluster 2: 41 to 80 artworks, and many others… (about this cluster – measurement, see under). Realizing the quantity t of artists in every cluster x,  then the ratio y = t / T  may be plotted in a diagram y-x. Fig.1 reveals the outcomes of those calculations for the 4 types.


Determine 1 Relative variety of artists y = t / T

producing an growing variety of artworks in x clusters

The dimensions-frequency diagram reveals the identical extremely uneven relationship for all 4 types: excessive frequency of artists who created a small variety of artworks and a lengthy tail of few artists who created extra or many extra artworks of the given fashion.

The asymmetry is typical for a lot of manufacturing processes with sources and merchandise (or objects)  in several fields: bibliography, communication and data within the media, scientific analysis, economics and finance. It has been analysed exhaustively in 2005 by Leo Egghe who prefers the inverse energy equation, generally known as the Lotka-law, above an exponential perform to explain this phenomenon mathematically (2).

 The Lotka-law:

f (x) = C / xa

the place f(x) is the size-frequency perform, C > 0 and a ≥ 0 are constants,

has the benefit that 1° the exponent a may be calculated as:

a = (2A – T) / (A – T)

and thus a ≈ 2 for A>>T (2, p.387), and that 2° it may be proved that C = 0,61 for a = 2 (2, p.14-16).

To the creator’s information, the Lotka-law with perform f(x) = y = relative frequency of artistswas for the primary time utilized in artwork historic analysis in 2015 (3). See additional a number of posts on this weblog (4).

Of curiosity at this level for the reason of the 4 WikiArt datasets are the exponent a = 2 as a result of in these datasets A >> T  and the noticed values of C = y for x = 1 (the intercept of the y-axis).

The values of Cin Fig.1 are 0,52; 0,54; 0,59 and 0,62, respectively for the 4 datasets. Clearly, these values depend upon the cluster-size ‘40’ chosen on this train: a better worth than ‘40’ would enhance the quantity t of artists in cluster 1 and thus end in larger values of the intercept. However since they’re near the theoretical worth C = 0,61, the chosen cluster-size appears appropriate and the frequent Lotka-law suits roughly the empirical information.

It permits for a ‘fast and soiled’ estimation of the sources (artists) who produced a variety of merchandise (artworks). Instance: for cluster 3 (81-120) – with a imply of 100 artworks – the Lotka-law yields y = t / T = 0,61 / 32 ≈ 0,068 or t = 0,068*T = 0,068*979 ≈ 66 artistsor about 7{f8ba1540c8ff36b18fce7f74ee82457b1a51a8aeff2be1c527e739d9453b5c55} of all artists collected in WikiArt. They produced collectively roughly 66*100 = 6600 artworks or about 10{f8ba1540c8ff36b18fce7f74ee82457b1a51a8aeff2be1c527e739d9453b5c55}of the entire A = 62362 of the 4 artwork types in WikiArt.


The counts of artists and their artworks collected and categorized within the 4 types Romanticism, Realism, Impressionism, Expressionism in WikiArt may be analysed and visualized in a y-x diagram. Thus a extremely advanced corpus of artwork historic information, unfold over two centuries, is offered in a unified description based mostly on the final strategy of a ‘manufacturing course of’ and the legislation of Lotka.

Might bigger samples than these of WikiArt falsify this empirical outcome ?



  1., the net house for visible arts from all world wide, a non-profit undertaking.

2.     Egghe L ‘Energy legal guidelines within the info manufacturing course of: Lotkaian informetrics’. Oxford: Elsevier. 2005, 427 pp.

3.      Bender Okay ‘Distant Viewing in Artwork Historical past. A Case Research of Inventive Productiveness’. Worldwide Journal for Digital Artwork Historical past (DAH-Journal), Concern n° 1, June 2015: 100-110.

4.     Newest software: February 23, 2022 105/ Historical past of my undertaking in progress (2): creative productiveness, the lengthy tail, the canon


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