Results¶

Two committed, fully reproducible benchmarks: a single deep block where all six methods (including the single-block-only topology optimizer) run head-to-head, and a settlement-scale region where the scalable methods are graded on the permeability-vs-displacement frontier.

One deep block, six methods¶

Block ZAF.9.3.1_1_40972 — the deepest block (by the depth proxy sqrt(n*A)/P) small enough for topology to run: 263 parcels, up to 7 rings deep, auto-picked with no hand tuning.

After, per method:

clearance_disp_depth	clearance_disp_perm	clearance_looped_disp_depth

clearance_looped_disp_perm	clearance_looped_perm_depth	clearance_looped_perm_perm

clearance_perm_depth	clearance_perm_perm	cycle_native_betweenness_contrast_disp_depth

cycle_native_betweenness_contrast_disp_perm	cycle_native_betweenness_contrast_perm_depth	cycle_native_betweenness_contrast_perm_perm

cycle_native_disp_depth	cycle_native_disp_perm	cycle_native_perm_depth

cycle_native_perm_perm	euclidean_grid_disp_depth	euclidean_grid_disp_perm

euclidean_grid_perm_depth	euclidean_grid_perm_perm	greedy_arterial_access_displacement_disp_depth

greedy_arterial_access_displacement_disp_perm	greedy_arterial_access_displacement_perm_depth	greedy_arterial_access_displacement_perm_perm

osm_footpaths_disp_depth	osm_footpaths_disp_perm	osm_footpaths_perm_depth

osm_footpaths_perm_perm	resistance_lp_disp_depth	resistance_lp_disp_perm

resistance_lp_perm_depth	resistance_lp_perm_perm	topology_disp_depth

topology_disp_perm	topology_perm_depth	topology_perm_perm

At each method's full build-out (terminal point of its permeability-vs-displacement frontier):

method	homes displaced	permeability
Topology	51.4%	97.7%
Least-Cost Tree	27.7%	94.8%
Looped Tree	67.2%	99.1%
Loop Network	19.9%	95.6%
Loop Network (desire-routed)	20.0%	96.4%
Direct Objective (LP)	20.0%	96.6%
Grid	37.4%	96.7%
Frontage (street-priced)	35.8%	98.8%
OSM Footpaths	25.7%	95.4%

Settlement scale: the `multiblock_depth_density` region¶

The depth_density metric tessellated and peeled the top 1,000 blocks of 83,192 by the cheap proxy, then grew the top-scoring block (ZAF.9.3.1_1_5810, peel depth 24) — growth added no neighbours, so the region is that single block of 6,619 parcels. Mean depth 24.0 rings, mean density 115 buildings/ha.

See the region on Google Maps

The `depth_density` screen across the Cape Town metro: the 1,000 blocks the fine pass scored, of 83,192, coloured by true peel depth. The count is the pre-filter budget, not an estimate of how many blocks are informal.

The permeability-vs-displacement frontier¶

Each method's permeability (a flow measure of how easily every parcel reaches a street) as cumulative road grows, against the displacement it costs:

Lens A — matched displacement: permeability bought at an equal home-cost¶

method	road (m)	homes displaced	permeability	note
Looped Tree	7,997	10.1%	78.8%
Grid	7,330	9.4%	89.2%	converged below budget
Loop Network	10,348	10.0%	92.5%
Loop Network (desire-routed)	14,663	10.0%	92.6%
Frontage (street-priced)	11,592	3.5%	82.1%	converged below budget
OSM Footpaths	3,094	1.4%	24.1%	converged below budget

Lens B — matched permeability: homes displaced to reach the standard¶

method	road (m)	homes displaced	permeability	note
Looped Tree	2,297	2.8%	60.8%
Grid	2,113	3.0%	65.6%
Loop Network	1,817	1.7%	66.9%
Loop Network (desire-routed)	1,762	0.7%	60.4%
Frontage (street-priced)	2,677	0.8%	60.5%
OSM Footpaths	3,094	1.4%	24.1%	target unreached

Each method on the ground¶

Same region, same access-depth colour scale (blue = at a street, red = deep), displaced buildings marked.

Lens A — matched displacement:

Looped Tree	Loop Network (desire-routed)

Loop Network	Grid

Frontage (street-priced)	OSM Footpaths

Lens B — matched permeability:

Looped Tree	Loop Network (desire-routed)

Loop Network	Grid

Frontage (street-priced)	OSM Footpaths

Reproduce¶

The whole benchmark — data, maps, curves, tables — regenerates from one self-logging command:

uv run python -m scripts.gen_example depth_density