A suite of allotaxonometric tools for the comparison of complex systems using rank-turbulence divergence

TL;DR

This paper introduces a set of tools for visually and quantitatively comparing complex systems through rank-turbulence divergence, enabling principled analysis of heavy-tailed distributions across multiple programming environments.

Contribution

It develops a comprehensive suite of allotaxonometric tools and visualizations based on rank-turbulence divergence for analyzing complex systems.

Findings

Provides visual comparison methods for heavy-tailed distributions

Supports multiple divergence measures including rank- and probability-turbulence divergences

Available in Matlab, Javascript, and Python for diverse use cases

Abstract

Describing and comparing complex systems requires principled, theoretically grounded tools. Built around the phenomenon of type turbulence, allotaxonographs provide map-and-list visual comparisons of pairs of heavy-tailed distributions. Allotaxonographs are designed to accommodate a wide range of instruments including rank- and probability-turbulence divergences, Jenson-Shannon divergence, and generalized entropy divergences. Here, we describe a suite of programmatic tools for rendering allotaxonographs for rank-turbulence divergence in Matlab, Javascript, and Python, all of which have different use cases.