Fractalopolis: A multi-scale scenario-modelling approach for evaluating master plans and rebalancing metropolitan hierarchy

Abstract

Metropolitan regions frequently exhibit hierarchical imbalances between central cores and peripheral subcentres, resulting in uneven accessibility, and service concentration. This paper presents Fractalopolis as a multi-scale scenario-modelling framework that encodes metropolitan hierarchy through the integration of fractal geometry, central-place logic, demographic allocation, and accessibility-based satisfaction indicators within a GIS environment. Applied to the Metropolitan City of Cagliari (Italy), a coastal-insular system characterised by strong edge effects and statutory environmental constraints, the model reproduces existing hierarchical gradients and evaluates alternative development scenarios through controlled amenity redistribution and residential additions. Results show that service-led reinforcement of peripheral nodes produces disproportionate improvements in suitability, whereas densification without proportional service upgrading yields limited gains. By embedding regulatory and ecological masking within hierarchical modelling, the study advances Fractalopolis toward a regulation-aware, transferable decision-support methodology for environmentally constrained metropolitan contexts.

Keywords

fractal urban morphology urban analytics accessibility modelling decision-support systems Fractalopolis Metropolitan City of Cagliari

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References

Batty

(2020) Defining complexity in cities Theories and Models of Urbanization: Geography, Economics and Computing Sciences. Springer, pp. 13–26.

Bouwman

(2000) Changing mobility patterns in a compact city: Environmental impacts. In: Compact Cities and Sustainable Urban Development: A Critical Assessment of Policies and Plans from an International Perspective. Aldershot: Ashgate 229–240. Available at: https://doi.org/10.4324/9781315189369-18

C40 Cities Climate Leadership Group (2021) How to build back better with a 15-minute city? Available at: https://www.c40knowledgehub.org/s/article/How-to-build-backbetter-with-a-15-minute-city (accessed 5 March 2026).

Calthorpe

(1993) The next American Metropolis: Ecology, Community, and the American Dream. Princeton Architectural Press.

Christaller

(1933/1980) Die zentralen Orte in Süddeutschland. G. Fischer. (Reprint: Wissenschaftliche Buchgesellschaft).

Czerkauer-Yamu

(2012) Strategic Planning for Developing Sustainable Metropolitan Areas with a Multiscale Decision Support System: The Vienna Case. PhD Thesis. Université de Franche-Comté.

Czerkauer-Yamu

, et al. (2013) Development of sustainable metropolitan areas using a multi-scale decision support system: fractalopolis model, accessibility evaluation and morphological rules. Working paper. Besançon: ThéMA, CNRS UMR 6049. Available at: https://halshs.archives-ouvertes.fr/hal-00837493/document (accessed 5 March 2026).

Deprêtre

Jacquinod

Barroca

, et al. (2024) Development of an Intensity of uses index to support design decision-making and improve urban development quality. Cities 147: 104779. https://doi.org/10.1016/j.cities.2023.104779

Emekci

(2022) From smart homes to smart cities: How smart homes contribute to the sustainable development goals. Smart Cities, Citizen Welfare, and the Implementation of Sustainable Development Goals. Hershey, PA: IGI Global, 321–337.

10.

Frankhauser

(2008) Fractal geometry for measuring and modeling urban patterns. In: Albeverio

, et al. (eds) The Dynamics of Complex Urban Systems: An Interdisciplinary Approach. Physica-Verlag (Springer), pp. 213–243.

11.

Frankhauser

(2012) The Fractalopolis Model - A Sustainable Approach for a Central Place System. Working paper. ThéMA Research Institute.

12.

Frankhauser

Bonin

(2024) Multifractal forward planning: the Fractalopolis model applied to the case of Greater Paris. In: SCIENCES Encyclopedia: Humanities and Social Sciences, Geography and Demography. ISTE Group.

13.

Frankhauser

Tannier

Vuidel

, et al. (2018) An integrated multifractal modelling to urban and regional planning. Computers, Environment and Urban Systems 67(1): 132–146. https://doi.org/10.1016/j.compenvurbsys.2017.09.011

14.

Frey

(2000) Not green belts but green wedges: the precarious relationship between city and country. Urban Design International 5(1): 13–25. https://doi.org/10.1057/palgrave.udi.9000003

15.

Garau

Alam

(2026) Scaling urban complexities and their influence on accessibility and spatial resilience. Journal of Urban Design 1–20. Available at: https://doi.org/10.1080/13574809.2026.2629313

16.

Healey

(2006) Relational complexity and the imaginative power of strategic spatial planning. European Planning Studies 14(4): 525–546. https://doi.org/10.1080/09654310500421196

17.

ISTAT (2022) Statistical data. Italian National Institute of Statistics.

18.

Jiang

, et al. (2024) Mapping liveability: The “15-min city” concept for car-dependent districts in Auckland, New Zealand. Applied Geography 163: 103197.

19.

Keith

Birch

Buchoud

NJA

, et al. (2023) A new urban narrative for sustainable development. Nature Sustainability 6(2): 115–117. https://doi.org/10.1038/s41893-022-00979-5

20.

Krier

(1998) Architecture: Choice or Fate. Papadakis Publisher.

21.

Kuttler

(2011) Climate change in urban areas. Part 2: measures. Environmental Sciences Europe 23: 21. https://doi.org/10.1186/2190-4715-23-21

22.

Logan

Hobbs

Conrow

, et al. (2022) The x-minute city: measuring the 10, 15, 20-minute city and an evaluation of its use for sustainable urban design. Cities 131: 103924. https://doi.org/10.1016/j.cities.2022.103924

23.

Manson

O’Sullivan

(2006) Complexity theory in the study of space and place. Environment and Planning A 38(4): 677–692. https://doi.org/10.1068/a37100

24.

Max-Neef

, et al. (1991) Human Scale Development: Conception, Application and Further Reflections. The Apex Press.

25.

Meerow

Newell

Stults

(2016) Defining urban resilience: a review. Landscape and Urban Planning 147: 38–49. https://doi.org/10.1016/j.landurbplan.2015.11.011

26.

Moreno

Allam

Chabaud

, et al. (2021) Introducing the “15-Minute city”: sustainability, resilience and place identity in future post-pandemic cities. Smart Cities 4: 93–111. https://doi.org/10.3390/smartcities4010006

27.

Mutzu Martis

, et al. (2024) A literature review of the Urban Heat Island (UHI) phenomenon connected with smart cities paradigm. International Conference on Computational Science and Its Applications. Cham: Springer, 3–17. Available at: https://doi.org/10.1007/978-3-031-65329-2_1

28.

Schwanen

Dijst

Dieleman

(2004) Policies for urban form and their impact on travel: the Netherlands experience. Urban Studies 41(3): 579–603. https://doi.org/10.1080/0042098042000178690

29.

Sepehri

Sharifi

(2025) X-minute cities as a growing notion of sustainable urbanism: a literature review. Cities 161: 105902. https://doi.org/10.1016/j.cities.2025.105902

30.

Simmonds

Coombe

(2000) The transport implications of alternative urban forms. In: Williams

Burton

Jenks

(eds). Achieving Sustainable Urban Form. London: E & FN Spon, 121–130.

31.

Torlini

, et al. (2025) Smart, close, and happy city: A global index for measuring urban well-being. The case study of the San Benedetto neighbourhood, Cagliari (Italy). International Conference on Computational Science and Its Applications. Cham Switzerland: Springer Nature, 69–87. Available at: https://doi.org/10.1007/978-3-031-97654-4_5

32.

Vuidel

, et al. (2012) Fractalyse 2.4 (software). Available at: https://fractalyse.org/ (accessed 05 03 2026).

33.

Wang

Liu

(2023) A classification-based multifractal analysis method for identifying urban multifractal structures considering geographic mapping. Computers, Environment and Urban Systems 101: 101952. https://doi.org/10.1016/j.compenvurbsys.2023.101952

34.

Yamu

, et al. (2015) Spatial accessibility to amenities, natural areas and urban green spaces: using a multiscale, multifractal simulation model for managing urban sprawl. Environment and Planning B: Planning and Design 42: 1054–1078. Available at: https://doi.org/10.1068/b130171

35.

Živanović

, et al. (2019) Urban system in Serbia-The factor in the planning of balanced regional development. Sustainability 11(15): 4168.

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