Beyond Static Boundaries: An Integrated Framework of Space Syntax, Fractals, and Spatial Clustering for Urban Agglomeration Dynamics

Firman Afrianto; Muhammad Sani Roychansyah; Yori Herwangi

doi:10.5614/jpwk.2026.37.1.2

Beyond Static Boundaries: An Integrated Framework of Space Syntax, Fractals, and Spatial Clustering for Urban Agglomeration Dynamics

Published: 2026-01-01 | DOI: 10.5614/jpwk.2026.37.1.2 | Vol 37, Issue 1 (2026)

Authors

Firman Afrianto

Doctoral Program in Urban and Regional Planning, Department of Architecture and Planning, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta, Indonesia

ORCID: 0000-0002-9369-8713 · OpenAlex: A5070893329

Muhammad Sani Roychansyah

Department of Architecture and Planning, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta,Indonesia

ORCID: 0000-0003-3721-8946 · OpenAlex: A5005078411

Yori Herwangi

Department of Architecture and Planning, Faculty of Engineering, Universitas Gadjah Mada, Yogyakarta,Indonesia

OpenAlex: A5054233431

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Abstract

Defining urban agglomeration boundaries using conventional administrative approaches often creates a ‘statistical illusion’ that distorts the functional spatial reality, while alternative dynamic models (such as cellular automata and agent-based models) are hindered by an absolute dependency on the availability of historical spatio-temporal data. Addressing this epistemological deadlock, this article proposes a new methodological framework that deconstructs the dynamics of metropolitan agglomeration evolution through the integration of space syntax, fractal dimension, and spatial clustering (DBSCAN) methods, purely by extracting the topological network of existing road intersections. This triadic framework addresses three fundamental analytical dimensions: space syntax diagnoses the ‘seeds’ of historical initiation (time-frame) through centrality metrics; fractal analysis quantifies the level of complexity and objectively establishes the threshold of evolutionary scale (scale-frame); and the DBSCAN algorithm visualizes the transition of agglomeration as an emergent spatial structure (visual-frame). The empirical implementation of the proof of concept was applied to the hierarchy of functional urban areas (FUA) in Indonesia, represented by the megalopolis of Jakarta and the metropolitan areas of Bandung and Yogyakarta. The precise calibration results successfully unveiled the ontological cycle of the city: from the discovery of micro-cluster embryos (postdiction) and mapping the explosion of fragmentation in the present (status quo) to determining the boundaries of macro fusion of urban areas in their entirety (prediction). In conclusion, this integrated framework shifts the paradigm from static delineation to process-oriented agglomeration analysis, offering an analytical instrument with extraordinary data efficiency that liberates spatial planning from the bias of arbitrary administrative jurisdictions.

Keywords

Urban Agglomeration; Space Syntax; Fractal Dimension; Spatial Clustering; Urban Morphology

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Research Intelligence

Data from OpenAlex ↗

Metrics

0.00

FWCIfield-weighted

28th

Percentilevs same year + field

Article

Work type

DIAMOND

Open Access

Topics

Urban Design and Spatial Analysis Primary

0.97

Building and Construction › Engineering › Physical Sciences

Urban Planning and Governance

0.00

Land Use and Ecosystem Services

0.00

Semantic Profile AI-classified research signals

Core Domains

Computer science 0.66

level 0

Urban agglomeration 0.47

level 2

Space (punctuation) 0.47

level 2

Secondary Topics

Cluster analysis 0.43 Theoretical computer science 0.42 Centrality 0.41 Scalability 0.40 Metropolitan area 0.39 Economies of agglomeration 0.37 Data mining 0.36 Dynamism 0.36 Hierarchy 0.32 Topology (electrical circuits) 0.32 Economic geography 0.32 Geography 0.32 Spatial network 0.31 Scale (ratio) 0.31 Artificial intelligence 0.29 Cellular automaton 0.29 Fractal 0.29 Urban planning 0.28 Empirical research 0.27 Data science 0.27 Resilience (materials science) 0.26 Contiguity 0.26

Institution Network

Universitas Gadjah Mada ID
Firman Afrianto · Muhammad Sani Roychansyah · Yori Herwangi

References

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Guo, Y., Zhu, J., & Liu, X. (2018). Implication of rural urbanization with place-based entitlement for social inequality in China. Cities, 82, 77–85. https://doi.org/10.1016/j.cities.2018.05.007 DOI: 10.1016/j.cities.2018.05.007
Hillier, B., & Hanson, J. (1984). The Social Logic of Space. Cambridge University Press. https://doi.org/10.1017/CBO9780511597237 DOI: 10.1017/cbo9780511597237
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[ref-1] Afrianto, F. (2023). Fractal Dimensions Analysis of Urban Agglomeration at Road Intersections in Metropolitan Malang Raya. IOP Conference Series: Earth and Environmental Science, 1186(1). https://doi.org/10.1088/1755-1315/1186/1/012010 DOI: 10.1088/1755-1315/1186/1/012010

[ref-2] Afrianto, F., Roychansyah, M. S., & Herwangi, Y. (2023). Bagaimana Kompleksitas Metropolitan di Indonesia? Sebuah Pengenalan Awal Dimensi Fraktal. PRANATACARA BHUMANDALA, 4(2). https://ejournal.unhi.ac.id/index.php/Pranatacara_Bhumandala

[ref-3] Alberti, M., McPhearson, T., & Gonzalez, A. (2018). Embracing Urban Complexity. In Urban Planet (pp. 45–67). Cambridge University Press. https://doi.org/10.1017/9781316647554.004 DOI: 10.1017/9781316647554.004

[ref-4] Batty, M. (2009a). Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies. In Encyclopedia of Complexity and Systems Science (131; pp. 1041–1071). Springer New York. https://doi.org/10.1007/978-0-387-30440-3_69 DOI: 10.1007/978-0-387-30440-3_69

[ref-5] Batty, M. (2009b). Complexity And Emergence In City Systems: Implications For Urban Planning. In Malaysian Journal of Environmental Management (Vol. 10, Issue 1).

[ref-6] Batty, M. (2021). Introduction to Urban Science. In Urban Book Series (pp. 11–14). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-981-15-8983-6_2 DOI: 10.1007/978-981-15-8983-6_2

[ref-7] Batty, M. (2022). Integrating space syntax with spatial interaction. Urban Informatics, 1(1). https://doi.org/10.1007/s44212-022-00004-2 DOI: 10.1007/s44212-022-00004-2

[ref-8] Batty, M., & Longley, P. (1994). Fractal Cities: A Geometry of Form and Function. Academic Press Limited.

[ref-9] Batty, M., & Longley, P. (1989). Urban growth and form: scaling, fractal geometry, and diffusion-limited aggregation. In Environment and Planning A (Vol. 21).

[ref-10] Batty, M., Morphet, R., Masucci, P., & Stanilov, K. (2014). Entropy, complexity, and spatial information. Journal of Geographical Systems, 16(4), 363–385. https://doi.org/10.1007/s10109-014-0202-2 DOI: 10.1007/s10109-014-0202-2

[ref-11] Billings, S. B., & Johnson, E. B. (2016). Agglomeration within an urban area. Journal of Urban Economics, 91, 13–25. https://doi.org/10.1016/j.jue.2015.11.002 DOI: 10.1016/j.jue.2015.11.002

[ref-12] Blanco, P. M., Madurga, S., Isvoran, A., Pitulice, L., & Mas, F. (2020). Fractal Dimension. In New Frontiers in Nanochemistry (pp. 171–186). Apple Academic Press. https://doi.org/10.1201/9780429022937-16 DOI: 10.1201/9780429022937-16

[ref-13] Blaudin de Thé, C., Carantino, B., & Lafourcade, M. (2021). The carbon ‘carprint’ of urbanization: New evidence from French cities. Regional Science and Urban Economics, 89, 103693. https://doi.org/10.1016/j.regsciurbeco.2021.103693 DOI: 10.1016/j.regsciurbeco.2021.103693

[ref-14] Cao, W., Dong, L., Wu, L., & Liu, Y. (2020). Quantifying urban areas with multi-source data based on percolation theory. Remote Sensing of Environment, 241. https://doi.org/10.1016/j.rse.2020.111730 DOI: 10.1016/j.rse.2020.111730

[ref-15] Chen, Y. (2010). Characterizing growth and form of fractal cities with allometric scaling exponents. Discrete Dynamics in Nature and Society, 2010. https://doi.org/10.1155/2010/194715 DOI: 10.1155/2010/194715

[ref-16] Chen, Y. (2012). Fractal dimension evolution and spatial replacement dynamics of urban growth. Chaos, Solitons and Fractals, 45(2), 115–124. https://doi.org/10.1016/j.chaos.2011.10.007 DOI: 10.1016/j.chaos.2011.10.007

[ref-17] Chen, Y. (2013). Fractal analytical approach of urban form based on spatial correlation function. Chaos, Solitons and Fractals, 49(1), 47–60. https://doi.org/10.1016/j.chaos.2013.02.006 DOI: 10.1016/j.chaos.2013.02.006

[ref-18] Chen, Y. (2020). Fractal modeling and fractal dimension description of urban morphology. Entropy, 22(9). https://doi.org/10.3390/e22090961 DOI: 10.3390/e22090961

[ref-19] Chen, Y., & Feng, J. (2012). Fractal-based exponential distribution of urban density and self-affine fractal forms of cities. Chaos, Solitons and Fractals, 45(11), 1404–1416. https://doi.org/10.1016/j.chaos.2012.07.010 DOI: 10.1016/j.chaos.2012.07.010

[ref-20] Fan, Q., Mei, X., Zhang, C., & Yang, X. (2022). Research on Gridding of Urban Spatial Form Based on Fractal Theory. ISPRS International Journal of Geo-Information, 11(12), 622. https://doi.org/10.3390/ijgi11120622 DOI: 10.3390/ijgi11120622

[ref-21] Fang, C., & Yu, D. (2017). Urban agglomeration: An evolving concept of an emerging phenomenon. Landscape and Urban Planning, 162, 126–136. https://doi.org/10.1016/j.landurbplan.2017.02.014 DOI: 10.1016/j.landurbplan.2017.02.014

[ref-22] Franklin, R. S., Delmelle, E. C., Andris, C., Cheng, T., Dodge, S., Franklin, J., Heppenstall, A., Kwan, M. P., Li, W. W., McLafferty, S., Miller, J. A., Munroe, D. K., Nelson, T., Öner, Ö., Pumain, D., Stewart, K., Tong, D., & Wentz, E. A. (2022). Making Space in Geographical Analysis. In Geographical Analysis. John Wiley and Sons Inc. https://doi.org/10.1111/gean.12325 DOI: 10.1111/gean.12325

[ref-23] Fujita, M., & Thisse, J.-F. (2002). Economic of Agglomeration: Cities, Industrial Location, and Regional Growth.

[ref-24] Giersch, Herbert., & Egon-Sohmen-Foundation. (1991). Towards a Market Economy in Central and Eastern Europe (H. Giersch, Ed.). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-76572-8 DOI: 10.1007/978-3-642-76572-8

[ref-25] Goffette-Nagot, F., & Schmitt, B. (1999). Agglomeration Economies and Spatial Configurations in Rural Areas. Environment and Planning A: Economy and Space, 31(7), 1239–1257. https://doi.org/10.1068/a311239 DOI: 10.1068/a311239

[ref-26] Griffiths, S., & Vaughan, L. (2020). Mapping spatial cultures: contributions of space syntax to research in the urban history of the nineteenth-century city. Urban History, 47(3), 488–511. https://doi.org/10.1017/S0963926820000206 DOI: 10.1017/s0963926820000206

[ref-27] Guo, Y., Zhu, J., & Liu, X. (2018). Implication of rural urbanization with place-based entitlement for social inequality in China. Cities, 82, 77–85. https://doi.org/10.1016/j.cities.2018.05.007 DOI: 10.1016/j.cities.2018.05.007

[ref-28] Hillier, B., & Hanson, J. (1984). The Social Logic of Space. Cambridge University Press. https://doi.org/10.1017/CBO9780511597237 DOI: 10.1017/cbo9780511597237

[ref-29] Maffenini, L., Moreno-Monroy, A., Schiavina, M., Veneri, P., (2019). GHSL-OECD Functional Urban Areas. KJ-NA-30001-EN-N (online). https://doi.org/10.2760/67415 (online) DOI: 10.2760/67415

[ref-30] Mandelbrot, B. B. (2004). Fractals and Chaos: Vol. C. Springer New York. https://doi.org/10.1007/978-1-4757-4017-2 DOI: 10.1007/978-1-4757-4017-2

[ref-31] McGee, T. G. (2009). The Spatiality of Urbanization: The Policy Challenges of Mega-Urban and Desakota Regions of Southeast Asia (161). https://www.researchgate.net/publication/237521773

[ref-32] McGee, T. G., & Shaharudin, I. (2016). Reimagining the “Peri-Urban” in the Mega-Urban Regions of Southeast Asia (pp. 499–516). https://doi.org/10.1007/978-3-319-28112-4_30 DOI: 10.1007/978-3-319-28112-4_30

[ref-33] Moreno-Monroy, A. I., Schiavina, M., & Veneri, P. (2021). Metropolitan areas in the world. Delineation and population trends. Journal of Urban Economics, 125. https://doi.org/10.1016/j.jue.2020.103242 DOI: 10.1016/j.jue.2020.103242

[ref-34] OECD. (2022). The OECD Metropolitan Database. http://stats.oecd.org/Index.aspx?DataSetCode=CITIES

[ref-35] Ortman, S. G., Lobo, J., & Smith, M. E. (2020). Cities: Complexity, theory and history. PLoS ONE, 15(12 December). https://doi.org/10.1371/journal.pone.0243621 DOI: 10.1371/journal.pone.0243621

[ref-36] Portugali, J. (2016). What Makes Cities Complex? In Complexity, Cognition, Urban Planning and Design (Vol. 1, pp. 3–19). the Springer Proceedings in Complexity book series (SPCOM). https://doi.org/10.1007/978-3-319-32653-5_1 DOI: 10.1007/978-3-319-32653-5_1

[ref-37] Portugali, J. (2021). Cities, complexity and beyond. In Handbook on Cities and Complexity. Edward Elgar Publishing.

[ref-38] Serra, M. L. L. A. (2013). ANATOMY OF AN EMERGING METROPOLITAN TERRITORY : Towards an Integrated Analytical Framework for Metropolitan Morphology [UNIVERSIDADE DO PORTO]. http://www.fe.up.pt

[ref-39] Shi, W., Batty, M., Goodchild, M., & Li, Q. (2022). The digital transformation of cities. Urban Informatics, 1(1). https://doi.org/10.1007/s44212-022-00005-1 DOI: 10.1007/s44212-022-00005-1

[ref-40] Shi, W., Goodchild, M. F., Batty, M., Kwan, M.-P., & Zhang, A. (2021). Urban Informatics (W. Shi, M. F. Goodchild, M. Batty, M.-P. Kwan, & A. Zhang, Eds.). Springer Singapore. https://doi.org/10.1007/978-981-15-8983-6 DOI: 10.1007/978-981-15-8983-6

[ref-41] Tu, X., Fu, C., Huang, A., Chen, H., & Ding, X. (2022). DBSCAN Spatial Clustering Analysis of Urban “Production–Living–Ecological” Space Based on POI Data: A Case Study of Central Urban Wuhan, China. International Journal of Environmental Research and Public Health, 19(9). https://doi.org/10.3390/ijerph19095153 DOI: 10.3390/ijerph19095153

[ref-42] van Nes, A., & Yamu, C. (2021a). Analysing Linear Spatial Relationships: The Measures of Connectivity, Integration, and Choice. In Introduction to Space Syntax in Urban Studies (pp. 35–86). Springer International Publishing. https://doi.org/10.1007/978-3-030-59140-3_2 DOI: 10.1007/978-3-030-59140-3_2

[ref-43] van Nes, A., & Yamu, C. (2021b). Introduction to Space Syntax in Urban Studies. In Introduction to Space Syntax in Urban Studies. Springer International Publishing. https://doi.org/10.1007/978-3-030-59140-3 DOI: 10.1007/978-3-030-59140-3

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