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

arXiv: https://arxiv.org/abs/2506.21808 · HTML: https://mlsanity.com/paper/2506.21808/

## Key facts

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- First posted on arXiv 26 Jun 2025.

## Abstract (arXiv)

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.