108/ 4 artwork kinds in numbers

Determine 1 Relative variety of artists y = t / T

producing an rising variety of artworks in x clusters

The scale-frequency diagram reveals the identical extremely uneven relationship for all 4 kinds: 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 type.

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

 The Lotka-law:

f (x) = C / x^a

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

has the benefit that 1° the exponent a might 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 data, the Lotka-law with operate 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 rely upon the cluster-size ‘40’ chosen on this train: a better worth than ‘40’ would improve the quantity t of artists in cluster 1 and thus end in greater values of the intercept. However since they’re near the theoretical worth C = 0,61, the chosen cluster-size appears appropriate and the widespread 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% of all artists collected in WikiArt. They produced collectively roughly 66*100 = 6600 artworks or about 10%of the entire A = 62362 of the 4 artwork kinds in WikiArt.

Conclusion

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

May bigger samples than these of WikiArt falsify this empirical end result ?

Notes

1. WikiArt.org, the net residence for visible arts from all world wide, a non-profit undertaking. https://www.wikiart.org/en/about

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

3.      Bender Ok ‘Distant Viewing in Artwork Historical past. A Case Research of Inventive Productiveness’. Worldwide Journal for Digital Artwork Historical past (DAH-Journal), Problem n° 1, June 2015: 100-110. https://www.academia.edu/13692791/Distant_Viewing_in_Art_History._A_Case_Study_of_Artistic_Productivity

4.     Newest software: February 23, 2022 105/ Historical past of my undertaking in progress (2): inventive productiveness, the lengthy tail, the canon https://kbender.blogspot.com/2022/02/105-history-of-project-in-progress-2.html?view=journal

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