On fractal dimensions of built and natural landcapes

Authors

  • Natalia Naoumova Universidade Federal de Pelotas. Faculdade de Arquitetura e Urbanismo
  • Andrei Bourchtein Universidade Federal de Pelotas. Instituto de Física e Matemática
  • Lioudmila Bourchtein Universidade Federal de Pelotas. Instituto de Física e Matemática

DOI:

https://doi.org/10.11606/issn.2317-2762.v21i36p174-193

Keywords:

Visual complexity. Fractals. Fractal analysis. Box-counting method. Natural landscape. Historic buildings

Abstract

In this study, fractal analysis is applied in the evaluation of the visual complexity of historic buildings and the surrounding natural environment. The fractal dimension and its approximations, quantified through the box-counting method, are used to define the general and local complexity of digital images of houses and landscapes. The essential properties of the box-counting method are discussed and an optimized version of the method is proposed. The hypothesis of the existence of a relationship between the complexity levels of built sites and natural landscapes is analyzed in the well-known case of the city of Amasya, and also for two historical cities in Brazil, Ouro Preto and Pelotas. The findings reveal a strong relationship between the spatial dynamics of fractal dimensions of built and natural environments.

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Author Biographies

  • Natalia Naoumova, Universidade Federal de Pelotas. Faculdade de Arquitetura e Urbanismo

    Graduada e mestre em Arquitetura e Urbanismo pela Universidade Federal do Leste, Rússia, doutora em Planejamento Urbano e Regional pela Universidade Federal do Rio Grande do Sul, professora da Faculdade de Arquitetura e Urbanismo da Universidade Federal de Pelotas (UFPEL).Faculdade de Arquitetura e Urbanismo da UFPEL

  • Andrei Bourchtein, Universidade Federal de Pelotas. Instituto de Física e Matemática

    Graduado e mestre em Matemática Aplicada pela Universidade Federal do Leste, Rússia, doutor em Matemática Aplicada e Computacional pelo Centro Hidrometeorológico da Rússia, professor do Instituto de Física e Matemática da
    Universidade Federal de Pelotas. Instituto de Física e Matemática da UFPEL

  • Lioudmila Bourchtein, Universidade Federal de Pelotas. Instituto de Física e Matemática

    Graduada e mestre em Matemática Pura pela Universidade Federal do Leste, Rússia, doutora em Matemática Pura pela Universidade Federal de São Petersburgo, Rússia, pesquisadora associada do Instituto de Física e Matemática da Universidade Federal de Pelotas. Instituto de Física e Matemática da UFPEL

References

BATTY, M.; LONGLEY, P. Fractal cities: a geometry of form and function. San Diego: Academic Press, 1994. 394 p.

BECHHOEFER, W.; BOVILL, C. Fractal analysis of traditional housing in Amasya, Turkey. Working Paper Series, University of California, v. 61, p. 1-21, 1994.

BOVILL, C. Fractal geometry in architecture and design. Boston: Birkhauser, 1996. 195 p.

BURKLE-ELIZONDO, G.; VALDEZ-CEPEDA, R. D. Fractal analysis of Mesoamerican pyramids. Nonlinear Dynamics, Psychology and Life Sciences. New York, v. 10, p. 105-122, 2006.

BUCZKOWSKI, S.; KYRIACOS, S.; NEKKA, F.; CARTILIER, L. The modified box-counting method analysis of some characteristic parameters. Pattern Recognition. Amsterdã, v. 31, p. 411-418, 1998. DOI: https://doi.org/10.1016/S0031-3203(97)00054-X

CAPO, D. The fractal nature of the architectural orders. Nexus Network Journal. Turim, v. 6, p. 30-40, 2004.

CARDILLO, A.; SCELLATO, S.; LATORA, S.; PORTA, S. Structural properties of planar graphs of urban street patterns. Physical Review E. Nova York, v. 73, p. 066107-1-066107-8, 2006.

CHEN, S. S.; KELLER, J. M.; CROWNOVER, R. M. On the calculation of fractal features from images.

IEEE Transactions on Pattern Analysis and Machine Intelligence. Los Alamitos, v. 15, p. 1087-1090, 1993. DOI: https://doi.org/10.1109/34.254066

DASILVA, D.; BOUDON, F.; GODIN, C.; PUECH, O.; SMITH, C.; SINOQUET, H. A critical appraisal of the box counting method to assess the fractal dimension of tree crowns. Lecture Notes in Computer Science. Berlim, v. 4291, p. 751–760, 2006.

FALCONER, K. J. Fractal geometry: mathematical foundations and applications. Chichester: Wiley, 2003. 400 p.

FOROUTAN-POUR, K.; DUTILLEUL, P.; SMITH, D. L. Advances in the implementation of the boxcounting method of fractal dimension. Applied Mathematics and Computation. Londres, v. 105, p.195-210, 1999. DOI: https://doi.org/10.1016/S0096-3003(98)10096-6.

FRANKHAUSER, P.; TANNIER, C. Fractalyse, 2012. Disponível em: http://www.fractalyse.org/enhome.html. Acesso em: 04 jun. 2014.

HAGERHALL, C. M.; PURCELL, T.; TAYLOR, R. Fractal dimension of landscape silhouette outlines as a predictor of landscape preference. Journal of Environmental Psychology. Amsterdã, v. 24, p. 247-255, 2004. DOI: https://doi.org/10.1016/j.jenvp.2003.12.004

HEATH, T.; SMITH, S. G.; LIM, B. Tall buildings and the urban skyline: the effect of visual complexity on preferences. Environment and Behavior. Thousand Oaks, v. 32, p. 541–556, 2000. DOI: https://doi.org/10.1177/00139160021972658.

JELINEK, H. F.; FERNANDEZ, E. Neurons and fractals: how reliable and useful are calculations of fractal dimensions?. Journal of Neuroscience Methods. Amsterdã, v. 81, p. 9-18, 1998. DOI: https://doi.org/10.1016/S0165-0270(98)00021-1.

JOYE Y. A review of the presence and use of fractal geometry in architectural design. Environment and Planning B. Londres, v. 38, p. 814-828, 2011. DOI: https://doi.or/10.1068/b36032.

KELLER, J. M.; CROWNOVER, R. M.; CHEN, R. Y. Characteristics of natural scenes related to the fractal dimension. IEEE Transactions on Pattern Analysis and Machine Intelligence. Los Alamitos, v. 9, p. 621-627, 1987.

LIANG, J.; HU, Y.; SUN, H. The design evaluation of the green space layout of urban squares based on fractal theory. Nexus Network Journal. Turim, v. 15, p. 33-49, 2013. DOI: https://doi.org/10.1007/s00004-012-0135-3

LORENZ, W. E. Fractals and fractal architecture. Vienna: Vienna University of Technology, 2002. 152 p.

MANDELBROT, B. The fractal geometry of nature. San Francisco: Freeman, 1982. 468 p.

MANDELBROT, B. Fractals and the rebirth of iteration theory. In: PEITGEN, H.-O.; RICHTER, P. H. (Eds). The beaty of fractals: images of complex dynamical systems. Berlim: Springer, 1986. 199 p.

MILOSEVIC, N. T.; RISTANOVIC, D. Fractal and nonfractal properties of triadic Koch curve. Chaos, Solitons and Fractals. Londres, v. 34, p. 1050-1059, 2007. DOI: 10.1016/j.chaos.2006.03.117

MOISY, F. Boxcount, 2008. Disponível em: http://www.mathworks.com/ matlabcentral/fileexchange/13063-boxcount. Acesso em: 04 jun. 2014.

OSTWALD, M. J. Fractal architecture: late twentieth century connections between architecture and fractal geometry. Nexus Network Journal. Turim, v. 3, p. 73-83, 2001. DOI: https://doi.org/10.1068/b38124

PEITGEN, H.-O.; JÜRGENS, H.; SAUPE, D. Chaos and fractals: new frontiers of science. New York: Springer, 2004. 864 p.

PERRY, S. G.; REEVES, R. W.; SIM, J. C. Landscape design and the language of nature. Landscape Review. Lincoln, v. 12, p. 3-18, 2008.

RODIN, V.; RODINA, E. The fractal dimension of Tokyo’s streets. Fractals. Singapura, v. 8, p. 413-418, 2000. DOI: https://doi.org/10.1142/S0218348X00000457.

STAMPS, A. E. Fractals, skylines, nature and beauty. Landscape and Urban Planning. Amsterdã, v. 60, p. 163-184, 2002. DOI: https://doi.org/10.1016/S0169-2046(02)00054-3

THOMAS, I.; FRANKHAUSER, P.; FRENAY, B.; VERLEYSEN, M. Clustering patterns of urban built-up areas with curves of fractal scaling behaviour. Environment and Planning B. Local, v. 37, p. 942-954, 2010. DOI: https://doi.org/10.1068/b36039

VAUGHAN, J.; OSTWALD, M. J. Using fractal analysis to compare the characteristic complexity of nature and architecture: re-examining the evidence. Architectural Science Review. Londres, v. 53, p. 323-332, 2010. DOI: https://doi.org/10.3763/asre.2010.0024

VOSS, R. Fractals in nature: from characterization to simulation. In: PEITGEN, H.-O.; SAUPE, D. (Eds.). The science of fractal images. New York: Springer, 1988. 326 p.

VYZANTIADOU, M. A.; AVDELAS, A. V.; ZAFIROPOULOS, S. The application of fractal geometry to the design of grid or reticulated shell structures. Computer-Aided Design. Berlim, v. 39, p. 51-59, 2007. DOI: https://doi.org/10.1016/j.cad.2006.09.004

ZACHARIAS, J. Preferences for view corridors through the urban environment. Landscape and Urban Planning. Amsterdã, v. 43, p. 217–225, 1999. DOI: https://doi.org/10.1016/S0169-2046(98)00104-2

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Published

2015-02-24

Issue

Vol. 21 No. 36 (2014)

Section

Artigos

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How to Cite

Naoumova, N., Bourchtein, A., & Bourchtein, L. (2015). On fractal dimensions of built and natural landcapes. Pós. Revista Do Programa De Pós-Graduação Em Arquitetura E Urbanismo Da FAUUSP, 21(36), 174-193. https://doi.org/10.11606/issn.2317-2762.v21i36p174-193