Fig 1.
Aburrá Valley and administrative units of the urban area of Medellín. Percentage of housing social stratum composition in each administrative unit in square brackets, from lower (1) to higher (6), estimated by the MEData report [18] (https://medata.gov.co/dataset/3ba48b35-29ff-4798-bd20-d4b41dc10f85). Elevation from USGS 1 arc-second resolution [19] (https://www.usgs.gov/3d-elevation-program). Official boundaries from World Bank (https://datacatalog.worldbank.org/) and Instituto Geográfico Agustín Codazzi (https://www.colombiaenmapas.gov.co/).
Fig 2.
Qualitative fractality in Medellín.
A) Planimetric system of Medellín. The origin of the Cartesian plane is defined as the intersection of the Aburrá River with the San Juan Avenue. From this origin, the four quadrants (and their visual order) are defined: SE (FF), SW (RFI), NE (HD), and NW (BOP). Target bridge intersections are highlighted in numbered squares. B) Emerging urban fractals at the intersections of the Aburrá River. The different visual orders in the urban landscape are determined by fieldwork and are portrayed in a color code to facilitate their identification by the composition of urban functions. Basemap data from the OpenStreetMap project [48] (https://planet.openstreetmap.org/) and GeoMedellín Open Data [49](https://www.medellin.gov.co/geomedellin/datosAbiertos/).
Table 1.
The planimetric visual order iterates at bridge-scale. The geographic reference where the planimetric visual order is observed as a distinctive combination of key urban functions within each bridge scene.
Fig 3.
State variables of the Medellín urban system.
A) Terrain curvature (Calculated from elevation map provided by USGS, https://www.usgs.gov/3d-elevation-program). B) Leaf Area Index (LAI, calculated from Sentinel 2 satellite images, https://dataspace.copernicus.eu/, following [61]). C) Ecological connectivity network. D) Hydrographic network. E) Trees. F) Residential system. G) Urban facilities. H) Public services networks. I) Public space. J) Pedestrian network. K) Urban structural axes. L) Road network. M) Public transport routes. N) Metro Transport System. O) Bike paths. Basemap C to D, from GeoMedellín Open Data [49] (https://www.medellin.gov.co/geomedellin/datosAbiertos/).
Fig 4.
Fractal classification dendrogram of the variables that define the urban state in Medellín.
Error is estimated as the standard deviation of the sample from bootstrapping.
Fig 5.
Spatial entropy for urban state variables in Medellín.
Maximum entropy corresponds to the homogeneous distribution of urban state variables across the i-th administrative units with area ai. The error is estimated using the standard deviation.
Fig 6.
Fluid representation of urban variables in Medellín.
A) Administrative map of Medellín. B) to P) Urban state variables ordered from higher to lower percentage deformation, in square brackets . Basemap source for state variables as in Fig 3.