{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/allotaxonometry-and-rank-turbulence","title":"Allotaxonometry and rank-turbulence divergence: A universal instrument for comparing complex systems","arxiv_id":"2002.09770","date":"2020-02-22","proceeding":null,"authors":["P. S. Dodds","J. R. Minot","M. V. Arnold","T. Alshaabi","J. L. Adams","D. R. Dewhurst","T. J. Gray","M. R. Frank","A. J. Reagan","C. M. Danforth"],"abstract":"Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce `allotaxonometry' along with `rank-turbulence divergence' (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram for rank-rank pairs with an ordered list of components according to divergence contribution. We explore the performance of rank-turbulence divergence, which we view as an instrument of `type calculus', for a series of distinct settings including: Language use on Twitter and in books, species abundance, baby name popularity, market capitalization, performance in sports, mortality causes, and job titles. We provide a series of supplementary flipbooks which demonstrate the tunability and storytelling power of rank-based allotaxonometry.","url_abs":"https://arxiv.org/abs/2002.09770v5","url_pdf":"https://arxiv.org/pdf/2002.09770v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"allotaxonometry-and-rank-turbulence","repo_url":"https://gitlab.com/compstorylab/allotaxonometer","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"allotaxonometry-and-rank-turbulence","repo_url":"https://github.com/compstorylab/covid19ngrams","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"allotaxonometry-and-rank-turbulence","repo_url":"https://github.com/compstorylab/storywrangling","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"allotaxonometry-and-rank-turbulence","repo_url":"https://github.com/jkbren/rank-turbulence-divergence","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"allotaxonometry-and-rank-turbulence","repo_url":"https://gitlab.com/compstorylab/covid19ngrams","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2002.09770","atlas_url":"https://app.syntology.ai/?focus=2002.09770","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}