Accessibility is not one-dimensional. The framework separates it into two spatial scales:
Proximity measures access to everyday services — grocery stores, pharmacies, cafés, schools — reachable on foot within short distances.
Opportunity measures access to city-scale resources — jobs, universities, stadiums, cultural venues — reachable via public transport within reasonable travel times.
The four zones
Each hexagonal cell in a city is classified based on whether its Proximity and Opportunity scores fall above or below the city-wide median:
Inclusion Above-median in both dimensions.
Spatial Isolation Good local services but poor transit connections.
Social Isolation Good transit but few local amenities.
Total Isolation Below-median in both dimensions.
The third dimension: Value
The paper also theorises a third axis — Value — capturing the quality and desirability of reachable services.
How to read the visualisation
The cartogram (left panel) shows the city divided into ~200 m hexagonal cells, coloured by their zone type. The scatter plot (right panel) places each hexagon by its Opportunity (x-axis) and Proximity (y-axis) scores.
Data & methods
Cities are covered with H3 resolution-9 hexagons (~200 m sides). Walking times via OSRM, public transport via GTFS + Connection Scan Algorithm. POIs from OpenStreetMap. Population from WorldPop.
Reading the scatter plot
Each dot is a hexagonal cell. Its position encodes:
X-axis (Opportunity): POIs reachable by public transport.
Y-axis (Proximity): POIs reachable on foot.
Dashed lines mark city-wide medians. Hover or click to cross-highlight.
The bottom-left cluster = hexagons with no transit stops within 15 min walk.
Reading the cartogram
Hexagons coloured by zone type. Size = resident population.
Green — Inclusion High prox + High opp
Blue — Spatial Isolation High prox + Low opp
Yellow — Social Isolation Low prox + High opp
Red — Total Isolation Low prox + Low opp
Proximity = walkable local services. Opportunity = transit access to city-wide resources.
Thresholds are city-wide medians — each city is measured against its own standard.
Click any hexagon to inspect. Hover to cross-highlight on scatter.