The Comparative Numerical Analysis of Nature and Architecture: A New Framework

The Comparative Numerical Analysis of Nature and Architecture: A New Framework

J. VAUGHAN M.J. OSTWALD 

University of Newcastle, Australia

Page: 
156-166
|
DOI: 
https://doi.org/10.2495/DNE-V12-N2-156-166
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

Maintaining or creating a visual relationship between the form of a building and its surrounding natural landscape is often cited as a crucial factor in producing designs that support psychological comfort or environmental sustainability. While multiple methods for the analysis of nature and architecture have developed over time, only a handful of past studies have ever attempted to quantitatively compare the geometric properties of nature to those of architecture. Fractal analysis provides one of the very few methods available to analyse and compare the geometry of diverse objects. The fractal dimension (D) of an object is a numerical value which reflects the volume and distribution of detail in an item. Of  the many subjects analysed using this method, the forms of nature (such as coastlines, rivers and plant elements) have been successfully measured, as have built forms (such as houses, public buildings and cityscapes). However, despite the method’s application to each subject area, few examples exist where fractal dimension data derived from nature are compared with equivalent architectural data. A primary reason cited for this situation is the disparity of methodological variables, in particular, representational approaches to the images used for comparison are presently disparate and uncategorised.

This paper responds to the existing lack of a comparable basis by analysing and categorising meth- odological examples from applications of fractal analysis to both natural and architectural cases. Specifically, the type of image delineation and the level of information contained in it are compared and ranked. Through this process, the paper provides a critical overview of the past application of fractal analysis to images, and thereby provides a starting framework for how the built and natural environ- ments might be rigorously compared in the future.

Keywords: 

fractal dimension, landscape analysis, visual complexity.

  References

[1] Kellert, S.R., Building for Life: Designing and Understanding the Human-Nature Con- nection, Island Press: Washington, 2012.

[2] Makhzoumi, J. & Pungetti, G., Ecological Landscape Design and Planning: the Medi- terranean Context, E & FN Spon: New York, 1999. http://dx.doi.org/10.4324/9780203223253

[3] Williams, D.E., Sustainable Design: Ecology, Architecture, and Planning. John Wiley & Sons: Hoboken, p. 320, 2007.

[4] Vaughan, J. & Ostwald, M.J., Nature and architecture: revisiting the fractal connection in Amasya and Sea Ranch. In Performative Ecologies in the Built Environment: Sus- tainability Research Across Disciplines, p. 42, 2009.

[5] Mandelbrot, B.B., The Fractal Geometry of Nature, Freeman: San Francisco, 1982.

[6] Bovill, C., Fractal Geometry in Architecture and Design, Birkhäuser: Boston, 1996.

[7] Camastra, F., Data dimensionality estimation methods: a survey. Pattern Recognition,

36(12), pp. 2945–2954, 2003. http://dx.doi.org/10.1016/S0031-3203(03)00176-6

[8] Ostwald, M.J. & Vaughan, J., Limits and errors: optimising image pre-processing stan- dards for architectural fractal analysis. ArS Architecture Science, 7, pp. 1–19, 2013.

[9] Vaughan, J. & Ostwald, M.J., Refining a computational fractal method of analysis: test- ing Bovill’s architectural data. In Proceedings of the 15th International Conference on Computer Aided Architectural Design Research in Asia, CAADRIA: Hong Kong, pp. 29–38, 2010.

[10] Ostwald, M.J., Vaughan, J. & Tucker, C., Architecture and Mathematics, From Antiq- uity to the Future, II: 1500s to the Future, ed. K. Williams, Birkhauser/Springer: Basel/ Cham, pp. 339–354, 2015. http://dx.doi.org/10.1007/978-3-319-00143-2_22

[11] Lorenz, W., Fractals and Fractal Architecture. Masters Diss, 2003.

[12] Morse, D.R., Lawton, J.H., Dodson, M.M. & Williamson, M.H., Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature, 314, pp. 731–733, 1985. http://dx.doi.org/10.1038/314731a0

[13] Spehar, B., Clifford, C.W.G., Newell, B.R. & Taylor, R.P., Universal aesthetic of frac- tals. Computers & Graphics, 27(5), pp. 813–820, 2003. http://dx.doi.org/10.1016/S0097-8493(03)00154-7

[14] Tucek, P., Marek, L., Paszto, V., Janoska, Z. & Dancak, M., Fractal perspectives of GIScience based on the leaf shape analysis. GeoComputation, pp. 169–176, 2011.

[15] Wahl, B., Larsen, M. & Roy, P.V., Exploring Fractals on the MacIntosh, Addison-Wes- ley Longman Publishing: Boston, 1994.

[16] Yang, Z.-Y. & Juo, J.-L., Interpretation of sieve analysis data using the box-counting method for gravelly cobbles. Canadian Geotechnical Journal, 38(6), pp. 1201–1212, 2001. http://dx.doi.org/10.1139/t01-052

[17] Perry, S.G., Reeves, R.W. & Sim, J.C., Landscape Design and the Language of Nature. Landscape Review, 12(2), pp. 3–18, 2008.

[18] 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 Intel- ligence, PAMI-9, pp. 621–627, 1987. http://dx.doi.org/10.1109/TPAMI.1987.4767956

[19] Stamps, A.E., Fractals, skylines, nature and beauty. Landscape and Urban Planning,

60(3), pp. 163–184, 2002. http://dx.doi.org/10.1016/S0169-2046(02)00054-3

[20] Hagerhall, C.M., Purcell, T. & Taylor, R.P., Fractal dimension of landscape silhouette outlines as a predictor of landscape preference. Journal of Environmental Psychology, 24(2), pp. 247–255, 2004. http://dx.doi.org/10.1016/j.jenvp.2003.12.004

[21] Robertson, L., A New Theory for Urban Design. Urban Design, 56, pp. 11–13, 1995.

[22] Batty, M. & Longley, P., Fractal Cities: A Geometry of Form and Function, Academic Press: San Deigo, 1994.

[23] Benguigui, L., Czamanski, D., Marinov, M. & Portugali, Y., When and where is a city fractal? Environment and Planning B: Planning and Design, 27(4), pp. 507–519, 2000. http://dx.doi.org/10.1068/b2617

[24] Brown, C.T. & Witschey, W.R.T., The fractal geometry of ancient Maya settlement. Journal of Archaeological Science, 30(12), pp. 1619–1632, 2003. http://dx.doi.org/10.1016/S0305-4403(03)00063-3

[25] Chalup, S., Henderson, N., Ostwald, M.J. & Wiklendt, L. A method for cityscape analy- sis by determining the fractal dimension of its skyline. In Innovation Inspiration and Instruction. eds N. Gu, L.F. Gul & M.J. Ostwald, pp. 337–344, 2008.

[26] Oleschko, K., Brambila, R., Brambila, F., Parrot, J.-F. & López, P., Fractal analysis of teotihuacan, Mexico. Journal of Archaeological Science, 27(11), pp. 1007–1016, 2000. http://dx.doi.org/10.1006/jasc.1999.0509

[27] Burkle-Elizondo, G. & Valdez-Cepeda, R.D., Fractal analysis of Mesoamerican pyra- mids. Nonlinear Dynamics, Psychology, and Life Sciences, 10(1), 105–122, 2006.

[28] Bechhoefer, W. & Bovill, C., Fractal analysis of traditional housing in Amasya, Turkey. Traditional Dwellings and Settlements Working Paper Series, 61, 1–21, 1994.

[29] Zarnowiecka, J.C., In search of new computer tools: what does Bovill really measure in architecture? In Connecting the Real and the Virtual – design e-ducation 20th eCAADe Conference Proceedings, pp. 342–345, 2002.

[30] Debailleux, L., Complementary approach for vernacular wooden frame structures reconstruction. In Digital Heritage, Springer: New York, pp. 441–449, 2010. http://dx.doi.org/10.1007/978-3-642-16873-4_35

[31] Wen, K.-C. & Kao, Y.-N., An analytic study of architectural design style by fractal dimension method. In Proceedings of the 22nd ISARC, pp. 1–6, 2005.

[32] Bechhoefer, W. & Appleby, M., Fractals, music and vernacular architecture: an experi- ment in contextual design. In Critical Methodologies in the Study of Traditional Envi- ronments. vol 97, ed. N Al. Sayyad, University of California at Berkeley: Berkeley pp. 1–33, 1997.

[33] Bourchtein, A., Bourchtein, B. & Naoumova N., On the visual complexity of built and natural landscapes. Fractals, 22, pp. 1450008–1450012, 2014. http://dx.doi.org/10.1142/S0218348X1450008X

[34] Wang, J. & Ogawa, S., Fractal analysis of colors and shapes for natural and urbans- capes. ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Suppl. W3 XL-7, pp. 1431–1438, 2015.

[35] Osmond, P., Hemispherical Photography as a Tool for Urban Sustainability Evaluation and Design, Social Science Research Network, 2010.

[36] Perry, S.G., The unfinished landscape fractal geometry and the aesthetics of ecological design, Queensland University of Technology, 2012.

[37] Ingegnoli, V., Landscape Ecology: A Widening Foundation, Springer Science: New York, 2013.

[38] Simon, R.M. & Simon, R.H., Mid-atlantic salt-marsh shorelines: mathematical com- monalities. Estuaries, 18(1), 199–206, 1995. http://dx.doi.org/10.2307/1352630