Paper Accepted in npj Complexity: The Complexity of Urban Verticality

Our paper “The Complexity of Urban Verticality” has been accepted for publication in npj Complexity, the Nature Portfolio journal dedicated to complex systems. Kudos to lead author Benny Chin (Wei Chien Benny Chin, now at the Department of Geography, National University of Singapore), a former Research Fellow of the group, who carried this work from the first idea to the accepted manuscript. The paper is co-authored with Michael Lees (Informatics Institute and Institute for Advanced Study, University of Amsterdam).

As cities increasingly grow in three dimensions, their vertical structure has become an important yet under-examined component of urban form. The paper introduces a spatial scaling framework that characterizes urban vertical complexity directly from Digital Surface Model and Digital Terrain Model data. A hierarchical quadtree representation generates a Total Absolute Difference (TAD) profile across successive scale levels, and the slope of the profile’s tail serves as the principal metric for comparing places. The framework is tested on nested windows in Canary Wharf, on 192 one-kilometer windows across three London zones, and on 17 standardized urban-zone windows in England. Across these analyses the TAD profiles share a shallow head followed by a steeper tail, with most of the variation in the tail regime; the tail slope is related to the tallest buildings but is not reducible to height alone. The result is a quantitative way of comparing how vertical structure is organized across different urban landscapes.

The Complexity of Urban Verticality
Chin WCB, Lees MH & Bouffanais R
npj Complexity, accepted for publication, 2026. [pdf]