The Limited Scaling Range of Empirical Fractals
David Avnir (1), Ofer Biham (1), Daniel A. Lidar (1,2), Ofer Malcai, (1) ((1) the Hebrew University of Jerusalem, Israel, (2) University of, California, Berkeley, USA)
TL;DR
This paper critically examines the limited scaling range observed in empirical fractal studies, challenging the assumption of widespread fractal abundance based on data.
Contribution
It provides a critical re-evaluation of the scaling range in empirical fractal reports, highlighting limitations in current understanding.
Findings
Empirical data shows a surprisingly limited scaling range in fractal measurements.
The abundance of fractals may be overestimated due to restricted scaling ranges.
The paper questions the general applicability of fractal models in empirical contexts.
Abstract
The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.
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Taxonomy
TopicsTheoretical and Computational Physics · Complex Systems and Time Series Analysis · Statistical Mechanics and Entropy