Fractal Dimensions in Architecture: Measuring the Characteristic Complexity of Buildings

In architectural research, debates about the development, function, or appropriateness of building forms have traditionally been dominated by qualitative approaches. These have been common in the past because the full geometric complexity of a building has proven difficult to encapsulate in any single measurement system. Even simple buildings may be made up of many thousands of separate changes in geometry, which combine together across multiple scales to create a habitable or functional structure. However, since the 1990s architectural scholars have begun to adopt one particular method for mathematically examining the form of a building. This method relies on fractal dimensions, which are measures of the characteristic complexity of an image, object, or set. This chapter introduces fractal dimensions and the primary method used to measure them in architecture, the box-counting approach. The chapter describes key methodological variables and limits that are pertinent to its application in architecture, and then it summarizes the results of past research using this approach. The paper concludes with a tabulated set of typical fractal dimension ranges for sets of plans and elevations of designs by 11 famous architects or practices.