{"title":"Fractals and the Korcak-law: a history and a correction","authors":"Attila R. Imre, Josef Novotný","doi":"10.1140/epjh/e2016-60039-8","DOIUrl":null,"url":null,"abstract":"<p>The Korcak-law – first presented in an empirical form in 1938 to describe the size-distribution of various geographical objects, including lakes and islands by Jaromír Kor?ák – was one of the examples used by Benoit Mandelbrot to show that fractals are not only mathematical monsters, but that they are applicable to describe many natural objects and phenomena too. In this paper, we would like to give a brief overview about the history of the Korcak-law and its connection to other similar rules. Moreover, we would like to show, that although there are similarities between fractal-related laws and the Korcak-law, the Korcak-exponent is not directly related to fractal dimension. In this sense, the measure introduced by Benoit Mandelbrot based on Kor?ák’s\tempirical findings is not a fractal measure.</p>","PeriodicalId":791,"journal":{"name":"The European Physical Journal H","volume":"41 1","pages":"69 - 91"},"PeriodicalIF":0.8000,"publicationDate":"2016-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1140/epjh/e2016-60039-8","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal H","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjh/e2016-60039-8","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 18
Abstract
The Korcak-law – first presented in an empirical form in 1938 to describe the size-distribution of various geographical objects, including lakes and islands by Jaromír Kor?ák – was one of the examples used by Benoit Mandelbrot to show that fractals are not only mathematical monsters, but that they are applicable to describe many natural objects and phenomena too. In this paper, we would like to give a brief overview about the history of the Korcak-law and its connection to other similar rules. Moreover, we would like to show, that although there are similarities between fractal-related laws and the Korcak-law, the Korcak-exponent is not directly related to fractal dimension. In this sense, the measure introduced by Benoit Mandelbrot based on Kor?ák’s empirical findings is not a fractal measure.
期刊介绍：
The purpose of this journal is to catalyse, foster, and disseminate an awareness and understanding of the historical development of ideas in contemporary physics, and more generally, ideas about how Nature works.
The scope explicitly includes:
- Contributions addressing the history of physics and of physical ideas and concepts, the interplay of physics and mathematics as well as the natural sciences, and the history and philosophy of sciences, together with discussions of experimental ideas and designs - inasmuch as they clearly relate, and preferably add, to the understanding of modern physics.
- Annotated and/or contextual translations of relevant foreign-language texts.
- Careful characterisations of old and/or abandoned ideas including past mistakes and false leads, thereby helping working physicists to assess how compelling contemporary ideas may turn out to be in future, i.e. with hindsight.
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