Fractal Analysis of architecture: determining the methodological limits.

    Josephine Vaughan,
    Michael J Ostwald,
    Stephan Chalup,
    Architecture and the environment


The box-counting variation of fractal analysis is the most common method for calculating the visual complexity of architecture. This computational approach provides a numerical value reflecting the amount of detail present in an elevation or plan of a building or urban space. As an approach for analysing city planning, urban layouts and architecture, the box-counting method has been employed in research and design by a wide range of scholars and designers for the last eighteen years. However, despite the volume of past research, the methodological limits, including the magnitude of potential error rates, are yet to be quantified. The lack of this information has lead to the present situation where often widely varying results are produced for the same image using ostensibly the same method. This makes it difficult to undertake comparisons of fractal dimensions calculated in past published research.

This paper, using architectural examples, tests known methodological anomalies present in the box-counting method to determine their numerical magnitude. Three architectural elevations are analysed by applying nine permutations of each of the three common factors causing errors in the results. These factors all relate to the presentation of the image data analysed and are commonly known as “line thickness”, “white space” and “image position”. The testing process produces twenty-seven results for each factor, providing eighty-one results overall which are compared with the “correct” or “optimal” results for the original architectural examples and then sorted to determine their relative impact on calculations.

The results of this analysis identify a standard range of settings for the initial architectural image data provided for analysis, reducing potential fluctuations in results by determining the methodological limits. This information is important because it ensures reliability and repeatability for future fractal analysis of the built environment.

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