Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

Iddo Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

Original languageEnglish (US)
Pages (from-to)30-40
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - May 15 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics


  • Fractality
  • Income
  • Lorenz curves
  • Power-laws
  • Rank distributions
  • Wealth


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