Allotaxonometry and rank-turbulence divergence: a universal instrument for comparing complex systems

EPJ Data Science

Table 1 A selection of example system comparisons producing a range of \(D^{\mathrm{R}}_{\alpha }(\Omega _{1} \| \Omega _{2})\) values

Systems \(\Omega ^{(1)}\) and \(\Omega ^{(2)}\)	Visualization/Section	α	\(D^{\mathrm{R}}_{\alpha }(\Omega _{1} \\| \Omega _{2})\)
Matching systems	Fig. 1B, Sect. 2.2	Any	0
Species, Barro Colorado Island	Fig. 3, Sect. 3.3	0	0.077
Causes of death, Hong Kong, 2012–2017	Flipbook S21, Sect. 4	1/3	0.213
Player season points, 2014–2015 vs 2015–2016	Flipbook S15, Sect. 4	1/3	0.279
Lowercase words, Harry Potter 7 vs vs 1–6	Flipbook S20, Sect. 4	1/2	0.308
Companies, 2007 vs 2018	Fig. 8, Sect. 3.5	1/3	0.441
Words on Twitter: 2016/11/09 vs 2017/08/13	Fig. 2, Sect. 3.1	1/3	0.493
Baby boy names, US, 1885 vs 1910	Sect. 3.4	∞	0.536
Baby girl names, US, 1900 vs 1925	Sect. 3.4	∞	0.631
Baby boy names, US, 1918 vs 1968	Flipbook S6, Sect. 3.4	∞	0.772
Baby boy names, US, 1968 vs 2018	Fig. 5, Sect. 3.4	∞	0.850
Baby girl names, US, 1918 vs 1968	Flipbook S5, Sect. 3.4	∞	0.887
Baby girl names, US, 1968 vs 2018	Fig. 4, Sect. 3.4	∞	0.926
Disjoint systems	Fig. 1D, Sect. 2.2	Any	1