Year: 2025
Type: article
Abstract: Innovation is distributed unevenly across space, yet the mechanisms behind persistent patenting inequality are poorly understood. Analyzing over a century of georeferenced U.S. patent data across eight major technological domains, we identify three consistent spatial patterns: (1) Zipfian scaling in patent output, (2) fractal clustering of innovation hubs, and (3) a 20-km scale of maximal spatial disparity, which we term the “inequality horizon.” These general patterns suggests that the geography of innovation emerges not only from urbanization or policy but from underlying generative principles. A minimal spatial model combining local reinforcement and long-range diffusion replicates all observed patterns without sector-specific assumptions. Analytical results show that the inequality horizon arises at the spatial scale where cluster growth balances internal heterogeneity. Our multiscale analysis suggest that emergent inequality in U.S. patenting stems by the interaction of urban scaling (superlinear productivity linked to city size) and fractal clustering (hierarchical spatial organization beyond administrative boundaries), pointing to general mechanisms governing the spatial dynamics of innovation.
Source: npj Complexity
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
SDG: Reduced inequalities
Open Access status: gold
Estimated APC paid: $2,690
Funders: Innovationsfonden, Joint Programming Initiative Water challenges for a changing world, Ministerio de Ciencia, Innovación y Universidades, Biodiversa+, European Commission, Agence Nationale de la Recherche, Naturvårdsverket, Horizon 2020 Framework Programme, Fundação para a Ciência e a Tecnologia, Agencia Estatal de Investigación
Awards: G1281928558, G2262748287, Beatriu de Pinos-3 Postdoctoral Programme, G259785605, G2841865453, Promoting & implementing joint programming to reinforce transnational research for the conservation and restoration of degraded ecosystems and their biodiversity, including a focus on aquatic systems, G3480869486, G3535982825, G3681454997, G3783317134, G4042783231, G4043177806, G425668148, G4725750110, G4937468798, G5080475149, G5404395142, G5605440823, G586857820, G6731524417, G683931746, G7084143925, G7489659912, G7805626310, G7863371703, G8153271282, G8497050386
OpenAlex ID: W4415780674