The Maximum Entropy principle and the nature of fractals
R. Pastor-Satorras (Dept. Fisica Fonamental, Univ. de Barcelona, and, Dept. of EAPS, MIT) J. Wagensberg (Museu de la Ciencia de Barcelona)
TL;DR
This paper applies the Maximum Entropy principle to deterministic fractals, providing a new statistical framework to characterize their scaling laws and fractal dimensions based on information content constraints.
Contribution
It introduces a novel approach using the Maximum Entropy principle to statistically describe fractals and their dimensions, linking information content to fractal properties.
Findings
Fractal scaling laws are explained via entropy constraints.
A new statistical characterization of fractals is proposed.
Fractal dimension is linked to information content.
Abstract
We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in those patterns. This constraint allows for a new statistical characterization of fractal objects and fractal dimension.
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