Skip to main content

From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts

  • Chapter
  • First Online:
Computational Approaches for Urban Environments

Part of the book series: Geotechnologies and the Environment ((GEOTECH,volume 13))

Abstract

Fractal geometry can be used to develop a multiscale approach to investigate the spatial organization of urban fabrics. First, the concepts behind fractal reference models are introduced so as to provide a better understanding of the results obtained from empirical analyses of urban patterns. Then, different methods for conducting fractal analyses are presented and the results obtained for urban patterns are discussed. It turns out that, despite their irregular appearance, urban patterns are often organized by an inherent fractal order principle, at least across a certain range of scales. More detailed analysis of the findings reveals links between these fractal properties and the historical contexts in which cities or urban districts developed. The influence of specific urban planning concepts on fractal behavior may also be identified, whereas the national context has less of a hold.

Urban fabrics emerge from complex interactions among various types of decision makers and are, in most cases, the outcome of a self-organizing process. However, by considering particular features of such urban fabrics and by comparing them with social demand and against certain planning concepts, a new planning concept can be proposed based on fractal logic, but intended for the sustainable development of metropolitan areas without excluding periurbanization. Software tools are presented for developing and evaluating scenarios for further urbanization of metropolitan areas.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The free software “fractalyse” was developed at the THEMA institute (Besançon) by Gilles Vuidel. A version allowing GIS-data to be used directly is currently under development.

References

  • Ariza-Villaverde AB, Jimenez-Hornero FJ, De Rave EG (2013) Multifractal analysis of axial maps applied to the study of urban morphology. Comput Environ Urban Syst 38:1–10

    Article  Google Scholar 

  • Bairoch P (1985) De Jericho à Mexico. Gallimard, Paris

    Google Scholar 

  • Batty M (2005) Cities and complexity: understanding cities with cellular automata, agent-based models, and fractals. MIT Press, Cambridge, MA

    Google Scholar 

  • Batty M, Kim SK (1992) Form follows function: reformulating urban population density functions. Urban Stud 29(7):1043–1070

    Article  Google Scholar 

  • Batty M, Longley P (1986) The fractal simulation of urban structure. Environ Plan A 18:1143–1179

    Article  Google Scholar 

  • Batty M, Longley P (1994) Fractal cities. A geometry of form and function. Academic, London

    Google Scholar 

  • Batty M, Xie Y (1996) Preliminary evidence for a theory of the fractal city. Environ Plan A 28:1745–1762

    Article  Google Scholar 

  • Benguigui L, Czamanski D, Marinov M, Portugali Y (2000) When and where is a city fractal? Environ Plan B 27(4):507–519

    Article  Google Scholar 

  • Berry BJ, Pred A (1961) Central place studies: a bibliography of theory and applications. Regional Science Research Institute, Philadelphia

    Google Scholar 

  • Bishop C (2006) Pattern recognition and machine learning. Springer, Berlin

    Google Scholar 

  • Breheny MJ (1997) Urban compaction: feasible and acceptable? Cities 14:209–217

    Article  Google Scholar 

  • Brun J, Fagnani J (1994) Lifestyles and locational choices—trade-offs and compromises: a case-study of middle-class couples living in the Ile-de-France region. Urban Stud 31(6):921–934

    Article  Google Scholar 

  • Calthorpe P (1993) The next American metropolis. Princeton Architectural Press, Princeton

    Google Scholar 

  • Cavailhès J, Frankhauser P, Peeters D, Thomas I (2004) Where Alonso meets Sierpinski: “an urban economic model of fractal metropolitan area”. Environ Plan A 36:550–578

    Article  Google Scholar 

  • Chen Y (2009) A new model of urban population density indicating latent fractal structure. Int J Urban Sustain Dev 1(1–2):89–110

    Google Scholar 

  • Chen Y, Feng J (2010) Spatiotemporal evolution of urban form and landuse structure in Hangzhou, China: evidence from fractals. Environ Plan B 37:838–856

    Article  Google Scholar 

  • Chen Y, Wang J (2013) Multifractal characterization of urban form and growth: the case of Beijing. Environ Plan B 40:884–904

    Article  Google Scholar 

  • Clark WAV (1968) Consumer travel patterns and the concept of Range. Ann Assoc Am Geogr 58(2):386–396

    Article  Google Scholar 

  • Czerkauer C (2012) Strategic planning for developing sustainable metropolitan areas with a multiscale decision support system. The Vienna case. PhD thesis, Université de Franche-Comté

    Google Scholar 

  • Czerkauer-Yamu C, Frankhauser P (2013) Development of sustainable metropolitan areas using a multiscale decision support system. Working paper, HALSHS: hal-00837493

    Google Scholar 

  • De Keersmaecker ML, Frankhauser P, Thomas I (2003) Using fractal dimensions for characterizing intra-urban diversity: the example of Brussels. Geogr Anal 35(4):310–328

    Article  Google Scholar 

  • Dubois-Taine G, Chalas Y (eds) (1997) La ville émergente. La Tour d’Aigue, Edition de l’Aube

    Google Scholar 

  • Eberstadt R, Möhring B, Petersen R (1910) Gross-Berlin. Ein Programm für die Planung der neuzeitlichen Grosstadt. Wasmuth, Berlin

    Google Scholar 

  • Fouchier V (1995) La densification: une comparaison internationale entre politiques contrastées. Les Annales de la Recherche Urbaine 67:95–108

    Google Scholar 

  • Frankhauser P (1994) La fractalité des structures urbaines. Anthropos, Paris

    Google Scholar 

  • Frankhauser P (1998) The fractal approach. A new tool for the spatial analysis of urban agglomerations. Population: an English selection, Special issue New Methodological Approaches in Social Sciences, pp 205–240

    Google Scholar 

  • Frankhauser P (2000) La fragmentation des espaces urbains et périurbains—une approche fractale. In: Derycke PH (ed) Structures des villes, entreprise et marchés urbains. L’Harmattan, Paris, pp 25–54

    Google Scholar 

  • Frankhauser P (ed) (2003) Morphologie des “villes émergentes” en Europe à travers les analyses fractales. Report, Université de Franche-Comté, UMR 6049 Théma

    Google Scholar 

  • Frankhauser P (2004) Comparing the morphology of urban patterns in Europe: a fractal approach. In: Borsdorf A, Zembri P (eds) European cities structures insights on outskirts: structures. European Cooperation in the Field of Scientific and Technical Research, Bruxelles, pp 93–103

    Google Scholar 

  • Frankhauser P (2005) La morphologie des tissus urbains et périurbains à travers une lecture fractale. Revue Géographique de l’Est XLV(3/4):145–160

    Google Scholar 

  • Frankhauser P (2008) Fractal geometry for measuring and modelling urban patterns. In: Albeverio S, Andrey D, Giordano P, Vancheri A (eds) The dynamics of complex urban systems—an interdisciplinary approach. Springer, Heidelberg, pp 241–243

    Google Scholar 

  • Frankhauser P (2012) The Fractalopolis model—a sustainable approach for a central place system. Working paper HALSHS: hal-00758864

    Google Scholar 

  • Frankhauser P (2013) La ville fractale—un concept d’aménagement multi-échelle. In: Brun G (ed) Ville et mobilité—Nouveaux regards de la recherche. Documentation française, Paris, pp 85–99

    Google Scholar 

  • Frankhauser P, Sadler R (1991) Fractal analysis of agglomerations. In: Hilliges M (ed) Natural structures: principles, strategies, and models in architecture and nature. University of Stuttgart, Stuttgart, pp 57–65

    Google Scholar 

  • Frankhauser P, Tannier C, Vuidel G, Houot H (2008) Une approche multi-échelle de l’accessibilité pour maîtriser l’étalement urbain, actes en ligne du Colloque mobil. TUM, Munich, 19 p. http://www.bfhz.uni-muenchen.de/cms/upload/downloads/Tagung-TUM-2008-Frankhauser-etal.pdf

  • Frankhauser P, Tannier C, Vuidel G, Houot H (2011) Une approche multi-échelle pour le développement résidentiel des nouveaux espaces urbains. In: Antoni JP (ed) Modéliser la ville. Forme urbaine et politiques de transport. Economica, Paris, pp 306–332

    Google Scholar 

  • Gault G, Bedeau L (eds) (2007) Les Français et leur habitat—Perception de la densité et des formes d’habitat, Principaux enseignements du sondage réalisé pour l’Observatoire de la Ville du 10 au 12 janvier 2007. TNS Sofres, Département Stratégies d’Opinion/Société, http://www.observatoiredelaville.com/pdf/Synthesesondage.pdf

  • Goodchild M, Mark D (1987) The fractal nature of geographic phenomena. Ann Assoc Am Geogr 77(2):265–278. doi:10.1111/j.1467-8306.1987.tb00158.x

    Article  Google Scholar 

  • Gordon P, Richardson HW (1997) Are compact cities a desirable planning goal? J Am Plan Assoc 63:95–106

    Article  Google Scholar 

  • Grassberger P, Procaccia I (1983) Measuring the strangeness of a strange attractor. Phys D 9:189–208

    Article  Google Scholar 

  • Güldner H (1968) Unsere Stadt – Tragödie einer Spätkultur. Beig-Verlag, Pinneberg

    Google Scholar 

  • Guo J, Bhat C (2002) Residential location modeling: accommodating sociodemographic, school quality and accessibility effects. University of Texas, Austin

    Google Scholar 

  • Jiang S, Liu D (2012) Box-counting dimension of fractal urban form: stability issues and measurement design. Int J Artif Life Res 3(3):521–525

    Article  Google Scholar 

  • Lam N, de Cola L (2002) Fractals in geography. The Blackburn Press, Caldwell

    Google Scholar 

  • Le Corbusier (1971) La Charte d’Athènes. Entretien avec les étudiants des écoles d’architecture. Éditions du Seuil, Paris, 190 p

    Google Scholar 

  • Leduc A, Prairie Y, Bergeron Y (1994) Fractal dimension estimates of a fragmented landscape: sources of variability. Landsc Ecol 9(4):279–286

    Article  Google Scholar 

  • Lerman SR (1976) Location, housing, automobile ownership, and mode to work: a joint choice model. Transp Res Rec 610:5–11

    Google Scholar 

  • Levinson DM, Kumar A (1994) The rational locator: why travel times have remained stable. J Am Plan Assoc 60:319–332

    Article  Google Scholar 

  • Mandelbrot B (1982) The fractal geometry of nature. Freeman, San Francisco

    Google Scholar 

  • McDowell L (1997) The new service class: housing, consumption and lifestyle among London bankers in the 1990s. Environ Plan A 29:2061–2078

    Article  Google Scholar 

  • McLachlan G, Peel D (2000) Finite mixture models. Wiley, New York

    Book  Google Scholar 

  • Newman PWG, Kenworthy JR (1989) Cities and automobile dependence: an international sourcebook. Gower, Aldershot/Brookfield

    Google Scholar 

  • Mohajeri N, French J, Batty M (2013) Evolution and entropy in the organisation of urban street patterns. Ann GIS 19:1–16

    Article  Google Scholar 

  • Palmer M (1988) Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75:91–102

    Article  Google Scholar 

  • Rodrigue J-P (2013) The geography of transport systems. Routledge, New York

    Google Scholar 

  • Salingaros N (2003) Connecting the fractal city. Key note speech, Biennial of Towns and Town planners in Europe, Barcelona. http://zeta.math.utsa.edu/~yxk833/connecting.html

  • Schöfl G (1986) Minimalnetze. ARCUS 2

    Google Scholar 

  • Schwanen T, Dijst M, Dieleman FM (2004) Policies for urban form and their impact on travel: the Netherlands experience. Urban Stud 41(3):579–603

    Article  Google Scholar 

  • Shen G (2002) Fractal dimension and fractal growth of urbanized areas. Int J Geogr Inf Sci 16(5):519–437

    Article  Google Scholar 

  • Sievert T (1997) Zwischenstadt. Bauwelt Fundamente 118

    Google Scholar 

  • Tannier C, Frankhauser P, Houot H, Vuidel G (2006) Optimisation de l’accessibilité aux aménités urbaines et rurales à travers le développement de modèles fractals d’urbanisation. In: XIIème colloque de l’ASRDLF, XIIème colloque du Grerbam, Sfax, Conference proceedings on CD

    Google Scholar 

  • Tannier C, Vuidel G, Frankhauser P, Houot H (2010) Simulation fractale d’urbanisation – MUP-city, un modèle multi-échelle pour localiser de nouvelles implantations résidentielles. Revue internationale de géomatique 20(3):303–329

    Article  Google Scholar 

  • Tannier C, Thomas I, Vuidel G, Frankhauser P (2011) A fractal approach to identifying urban boundaries. Geogr Anal 43(2):211–227

    Article  Google Scholar 

  • Tannier C, Vuidel G, Houot H, Frankhauser P (2012) Spatial accessibility to amenities in fractal and nonfractal urban patterns. Environ Plan B 39:801–819. doi:10.1068/b37132

    Article  Google Scholar 

  • Thomas I, Frankhauser P, Biernacki C (2008a) The morphology of built-up landscapes in Wallonia (Belgium): a classification using fractal indices. Landsc Urban Plan 84:99–115

    Article  Google Scholar 

  • Thomas I, Tannier C, Frankhauser P (2008b) Is there a link between fractal dimensions and other indicators of the built-up environment at a regional level. Cybergeo 413:24. http://www.cybergeo.eu/index16283.html

  • Thomas I, Frankhauser P, Frenay B, Verleysen M (2010) Clustering patterns of urban built-up areas with curves of fractal scaling behavior. Environ Plan B 37(5):942–954

    Article  Google Scholar 

  • Thomas I, Frankhauser P, Badariotti D (2012) Comparing the fractality urban districts: do national processes matter in Europe? J Geogr Syst 14(2):189–208. doi:10.1007/s10109-010-0142-4

    Article  Google Scholar 

  • Tourneux FP (2006) L’évolution de l’occupation du sol dans les franges franciliennes: des artificialisations concentrées plus qu’un étalement urbain? In: Larceneux A, Boiteux-Orain C (eds) Paris et ses franges: étalement urbain et polycentrisme. Editions universitaires de Dijon, Dijon, p 101

    Google Scholar 

  • Vanneste D, Thomas I, Vanderstraeten L (2008) The spatial structure(s) of the Belgian housing stock. J Hous Built Environ 23(3):173–198

    Article  Google Scholar 

  • Vicsek T (1989) Fractal growth phenomena. World Scientific, Singapore

    Book  Google Scholar 

  • Von Hoffman A, Felkner J (2002) The historical origins and causes of urban decentralization in the United States. Joint Center for Housing Studies, Harvard University, Cambridge, MA (WP 02–1)

    Google Scholar 

  • Weichhart P, Fassmann H, Hesina W (2005) Zentralität und Raumentwicklung, Nr. 167. Schriftenreihe der Österreichischen Raumordnungskonferenz, Wien

    Google Scholar 

  • White R, Engelen G (1994) Urban systems dynamics and cellular automata: fractal structures between order and chaos. Chaos Solitons Fractals 4(4):563–583

    Article  Google Scholar 

  • Wiel M, Tauty S, Rollier Y, Morvan A, Le Guirriec P, Desse RP, Barthélémy JP (1997) Comportement de mobilité et évolution de l’organisation urbaine (région urbaine de Brest). Etude pour la DRAST, la DTT, l‘UTP, le Plan urbain, Agence de développement et d’urbanisme du pays de Brest 2

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pierre Frankhauser .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Frankhauser, P. (2015). From Fractal Urban Pattern Analysis to Fractal Urban Planning Concepts. In: Helbich, M., Jokar Arsanjani, J., Leitner, M. (eds) Computational Approaches for Urban Environments. Geotechnologies and the Environment, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-11469-9_2

Download citation

Publish with us

Policies and ethics