The comparative numerical analysis of nature and architecture: a new framework

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 methodological 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 environments might be rigorously compared in the future.