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Are crowns of Betula pubescence Ehrh. fractal?

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Abstract

In this paper, the question whether crowns of downy birch, Betula pubescens Ehrh. are fractal is studied. The dependence of Σ (the number of branches with a length longer than L was studied for seven crowns. The method (Korák’s law) is justified for geometric and stochastic fractals. The sample is divided into classes according to Sturges. In the range of branch lengths L = 25–100 cm, all crowns exhibited properties of stochastic pseudofractals—structures that are characterized by significant linear regressions in coordinates logΣ vs. logL, five of seven with close dimensions D = 2.20–2.26. Elimination of outer bins from calculations is justified by the fact that any fractal is recognizable just in the middle scale range, when an element of the structure is already not seen and the entire structure is not covered by the field of vision. A technique for statistical processing of data is discussed and a criterion of internal consistency for the estimate of dimension D of a natural fractal is proposed.

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  1. Geological Institute, Kola Scientific Center, ul. Fersmana 14, Apatity, Murmansk oblast, 184209, Russia

    Yu. L. Voytekhovsky

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Voytekhovsky, Y.L. Are crowns of Betula pubescence Ehrh. fractal?. Paleontol. J. 48, 1315–1323 (2014). https://doi.org/10.1134/S0031030114120132

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  • DOI: https://doi.org/10.1134/S0031030114120132

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