Fractal-based description of urban form

Abstract

Fractals, shapes with nonintegral or fractional dimension which manifest similar degrees of irregularity over successive scales, are used to produce a consistent measure of the length of irregular curves such as coastlines and urban boundaries. The fractal dimension of such curves is formally introduced, and two computer methods for approximating curve length at different scales -- the structured walk and equipaced polygon methods -- are outlined. Fractal dimensions can then be calculated by performing log-log regressions of curve length on various scales. These ideas are tested on the urban boundary of Cardiff, and this reveals that the fractal dimension lies between 1.23 and 1.29. The appropriateness of fractal geometry in describing man-made phenomena such as urban form is discussed in the light of these tests, but further research is obviously required into the robustness of the methods used, the relevance of self-similarity to urban development, and the variation in fractal dimension over time and space.