Pathuk

Yogyakarta · Kampung kota

A kampung west of Malioboro with streets named after wayang figures. Most of its network is tagged living street rather than ordinary residential road.

Drive

Fig. 1 · r = 800 m — The drivable network inside the sampling disc. Uniform ink, no road-class hierarchy, no basemap: the shape is the subject.

Drive H 2.939 · φ 0.50

Orientation entropy: 2.939nat
H / H max: 0.820
φ orientation-order: 0.501
Circuity: 1.427~387
Average node degree: 2.26
Four-way: 5.5%
Dead-end: 34.7%
Intersection density: 150 /km²
Median segment length: 43 m
Network length: 32.8 km

H is in nats — the natural-log unit of information. That is why its maximum is ln 36 ≈ 3.584 rather than log₂ 36.

Circuity is an estimate: network distance over straight-line distance, averaged across a seeded sample of node pairs rather than across all of them. 387 pairs sampled · 106 pairs unreachable Pairs with no route between them at all are excluded from the mean. A large count means this network is fragmented — a signal about the data, not about the place.

Where these come from

Nodes: 545
Edges: 616
Intersections (degree ≥ 3): 301
Disc area: 2.01 km²
Intersection density: 150 /km²
Rose weighted length: 65.6 km
Per-edge circuity: 1.020

The intermediate values the column above is built from. Intersection density is the intersection count over the disc area; the weighted length is the denominator that turns a rose bar into a share. Two different circuity measures: the per-edge one compares each segment against its own chord, the sampled one compares distances between junctions. The first measures how much streets bend, the second how far out of your way the network takes you.

Walk

Fig. 2 · r = 800 m — The walkable network at the same centre, the same disc, the same extract. Every difference from the drawing beside it is the tag mapping, not a different place.

Walk H 2.985 · φ 0.47

Orientation entropy: 2.985nat
H / H max: 0.833
φ orientation-order: 0.471
Circuity: 1.395~461
Average node degree: 2.37
Four-way: 6.9%
Dead-end: 29.9%
Intersection density: 285 /km²
Median segment length: 36 m
Network length: 48.2 km

H is in nats — the natural-log unit of information. That is why its maximum is ln 36 ≈ 3.584 rather than log₂ 36.

Circuity is an estimate: network distance over straight-line distance, averaged across a seeded sample of node pairs rather than across all of them. 461 pairs sampled · 32 pairs unreachable Pairs with no route between them at all are excluded from the mean. A large count means this network is fragmented — a signal about the data, not about the place.

Where these come from

Nodes: 955
Edges: 1132
Intersections (degree ≥ 3): 574
Disc area: 2.01 km²
Intersection density: 285 /km²
Rose weighted length: 96.3 km
Per-edge circuity: 1.021

Both roses overlaid

Drive H 2.939 · φ 0.50Walk H 2.985 · φ 0.47

Each street segment’s bearing goes into one of 36 bins of 10°, weighted by length: a 500 m road counts ten times a 50 m gang. Bar length is the share of network length running that way, not a count of segments. The rose is always 180°-symmetric, because one segment traversed both ways differs by exactly 180°. Boeing 2019 §3

Drive
Walk
Both

DeltaWalk − Drive

Orientation entropy: +0.046
H / H max: +0.013
φ orientation-order: −0.030
Circuity: −0.032
Average node degree: +0.11
Four-way: +1.4%
Dead-end: −4.7%
Intersection density: +136
Median segment length: −7
Network length: +15.3

What walking adds

Walk-only length: 15.4 km
Share of walking network: 31.9%

Fig. 3 · r = 800 m — Ink: the edges that exist only in the walking network. Hairline: the network both modes share. Membership is decided by the tag mapping — an edge counts as walk-only when the OSM way it came from is not admitted to the driving network.

Rose as a table — 36 bins — Pathuk

Share of network length per 10° bearing bin, for drive and walk.
Bin	Bearing range	P — Drive	P — Walk	−P·ln P	−P·ln P
00	355°–5°	4.02%	4.42%	0.1292	0.1379
01	5°–15°	11.99%	10.86%	0.2543	0.2411
02	15°–25°	5.08%	5.03%	0.1514	0.1504
03	25°–35°	1.19%	1.38%	0.0527	0.0592
04	35°–45°	0.80%	0.66%	0.0386	0.0331
05	45°–55°	0.47%	0.54%	0.0252	0.0283
06	55°–65°	0.17%	0.19%	0.0107	0.0120
07	65°–75°	0.29%	0.29%	0.0170	0.0169
08	75°–85°	0.86%	0.98%	0.0409	0.0455
09	85°–95°	4.29%	5.02%	0.1352	0.1501
10	95°–105°	10.27%	9.67%	0.2337	0.2259
11	105°–115°	6.20%	6.32%	0.1724	0.1746
12	115°–125°	1.55%	1.60%	0.0645	0.0660
13	125°–135°	0.49%	0.40%	0.0261	0.0221
14	135°–145°	0.23%	0.30%	0.0140	0.0174
15	145°–155°	0.48%	0.47%	0.0258	0.0252
16	155°–165°	0.66%	0.72%	0.0333	0.0357
17	165°–175°	0.95%	1.14%	0.0444	0.0510
18	175°–185°	4.02%	4.42%	0.1292	0.1379
19	185°–195°	11.99%	10.86%	0.2543	0.2411
20	195°–205°	5.08%	5.03%	0.1514	0.1504
21	205°–215°	1.19%	1.38%	0.0527	0.0592
22	215°–225°	0.80%	0.66%	0.0386	0.0331
23	225°–235°	0.47%	0.54%	0.0252	0.0283
24	235°–245°	0.17%	0.19%	0.0107	0.0120
25	245°–255°	0.29%	0.29%	0.0170	0.0169
26	255°–265°	0.86%	0.98%	0.0409	0.0455
27	265°–275°	4.29%	5.02%	0.1352	0.1501
28	275°–285°	10.27%	9.67%	0.2337	0.2259
29	285°–295°	6.20%	6.32%	0.1724	0.1746
30	295°–305°	1.55%	1.60%	0.0645	0.0660
31	305°–315°	0.49%	0.40%	0.0261	0.0221
32	315°–325°	0.23%	0.30%	0.0140	0.0174
33	325°–335°	0.48%	0.47%	0.0258	0.0252
34	335°–345°	0.66%	0.72%	0.0333	0.0357
35	345°–355°	0.95%	1.14%	0.0444	0.0510
Sum = H				2.939	2.985

The last column is each bin’s term in H = −Σ P(i)·ln P(i). Add the thirty-six of them and you get the H printed under the rose. An empty bin contributes zero.

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Data jalan © OpenStreetMap contributors, ODbL 1.0. Basis data turunan ini ditawarkan dengan lisensi yang sama. · Boeing, G. 2019. Urban Spatial Order: Street Network Orientation, Configuration, and Entropy. Applied Network Science 4(1):67.