Fractals and the Korcak-law: a history and a correction

摘要

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 Jaromir Korcak - 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 Korcak's empirical findings is not a fractal measure.