URBAN SHAPES AS FRACTALS

Abstract

The fractal dimension of a curve provides a measure of its irregularity and if this dimension is stable over many scales, a single process is assumed to be generating the curve. Here we measure the fractal dimensions of curves defining the shape of the urban area of Cardiff during a period of its most rapid growth from 1886 to 1922. The results of applying the traditional scaling model suggest a new model in which fractal dimension varies with scale. Applications of this model show a decline in dimension over all scales and through time.