Using fractal analysis to compare the characteristic complexity of nature and architecture: re-examining the evidence

Abstract

Over the last few decades Complexity Scientists have shown that many natural systems possess similar geometric patterns that are repeated over multiple scales of observation. Using Euclidean geometry it is impossible to measure these forms as the closer the observer approaches the natural feature with a measuring device, the longer the result becomes. In response to this situation fractal geometry was developed as a means for determining, over progressive scales, the characteristic visual complexity of natural systems and forms. More recently it has been demonstrated that fractal geometry can also be useful for measuring the visual complexity of the constructed environment. As a result of this, it became possible, in the late 1990s to compare the fractal dimensions of both natural and constructed forms and thereby investigate the extent to which buildings are a reflection of their natural setting. The most famous examples of this provided evidence that a formal connection could be traced between the city of Amasya in Turkey and the landforms of its natural setting and a similar augment has been made about Sea Ranch in California. With only minimal evidence, a range of conclusions were drawn from this early work about the connection and influence of a local ecology on local architecture. The present paper re-tests these previous results using a more refined, computational version of the fractal analysis method and in doing so begins to explore the further application of this method for comparing natural and architectural forms.

Measuring visual attributes for assessing visual conflicts in urban environments

“…Keller et al (1987) Further to natural elements, it was found that the fractal geometry can also be useful for quantifying the properties of human creations such as art, architecture and the built environment (Mandelbrot, 1982). Several researchers have used fractal geometry to analyse different aspects of urban environments (Batty & Longley, 1994;Cooper & Oskrochi, 2008;Vaughan and Ostwald, 2010;Perry, 2012). However, Voss (1987) argued that fractal dimension is only appropriate for natural forms with large scales and natural boundaries.…”

“…Euclidean geometry developed around 300BC is unable to determine the size and complexity of any natural feature in the landscape (Vaughan and Ostwald, 2010). In response to this deficiency, fractal dimension was developed for the determination of complexity of natural systems (Vaughan and Ostwald, 2010).…”

“…Mandelbrot explained several methods to measure the dimensions of natural forms by fractal geometry (Vaughan and Ostwald, 2010). Mandelbrot (1982) considered particular natural forms which can be measured by the fractal dimension such as irregular natural shapes of rivers, lakes, trees, sky or galaxies.…”

“…In response to this deficiency, fractal dimension was developed for the determination of complexity of natural systems (Vaughan and Ostwald, 2010). Fractal geometry has a geometric order that is created from self-similarity and can describe and measure the self-similarity of natural forms (Perry, 2012).…”

“…After counting the number of filled boxes for each grid size, the comparison can be plotted on a log-log diagram to estimate the fractal dimension. The box-counting method was applied in numerous studies to measure the fractal dimension of architecture (Sala, 2002, Cooper and Oskorochi, 2008, Tucker, 2004, Vaughan and Ostwald, 2010 were are analysed using fractal dimension (Ostwald et al 2008, Ostwald and Vaughan, 2008. Ostwald and Vaughan (2010) also compared the nature and architecture using the fractal dimension to analyse relationships between architecture and its setting.…”