Fractals, Wealth Distributions, and Non-Euclidean Geometry: Quadrant Lorenz Curves
Year: 2026
Type: article
Abstract: Lorenz curves are a socioeconomic method of coding the statistics of positive-valued random variables. Standing at the confluence of fractals, wealth distributions, and non-Euclidean geometry, this paper presents quadrant Lorenz curves (QLCs): Lorenz curves whose shapes are that of the symmetric quarters of the p-norm unit circle. On the one hand, QLCs have a single parameter, and a clear geometric meaning. On the other hand, a comprehensive exploration establishes that QLCs display an assortment of socioeconomic and statistical behaviors. (1) They span a continuum of socioeconomic states ranging from perfect equality to perfect inequality, with three phase transitions along the continuum. (2) They display local rich fractality, local poor fractality, and double-Pareto tails. (3) They have inherent socioeconomic and statistical symmetries. The exploration includes a detailed socioeconomic-inequality analysis that illuminates QLCs from multiple inequality-indices `angles’. In a nutshell: QLCs manifest a novel class of `fractal’ statistical distributions, and the QLC features are unmatched by those of any other such class.
Source: Entropy
DOI: 10.3390/e28101085
Author: Iddo Eliazar
Institution: Tel Aviv University
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7215872018
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