Academic journal article Geographical Analysis

Using Fractal Dimensions for Characterizing Intra-Urban Diversity: The Example of Brussels

Academic journal article Geographical Analysis

Using Fractal Dimensions for Characterizing Intra-Urban Diversity: The Example of Brussels

Article excerpt

The objective of this paper is to compare fractal-based parameters calculated by different fractal methods for urban built-up areas and to link the observed spatial variations to variables commonly used in urban geography, urban economics, or land-use planning. Computations are performed on Brussels, Belgium. Two fractal methods (correlation and dilation) are systematically applied for evaluating the fractal dimension of built-up surfaces; correlation is used to evaluate the fractal dimension of the borders (lines). Analyses show that while fractal dimension is ideal for distinguishing the morphology of Brussels, each estimation technique leads to slightly different results. Interesting associations are to be found between the fractal dimensions and rent, distance, income, and planning rules. Despite its limitations, fractal analysis seems to be a promising tool for describing the morphology of the city and for simulating its genesis and planning. The model is robust: it replicates the urban spatial regularities and patterns, and could hence fruitfully be integrated into intra-urban simulation processes.

1. INTRODUCTION

Concepts of fractals, scaling, and fractal dimension have already widely been used in physical and human geography (e.g., Mandelbrot 1982; Goodchild and Mark 1987; Barnsley 1988 ; MacLennan et al. 1991). Let us begin by stating that fractals are objects whose geometric properties include irregularity, scale dependence., and self similarity. If spatial fractal analyses initially concentrated on "natural" objects, they were later extended to urban forms and urban systems, linking urban hierarchy to fractal geometry, or analyzing the "global" urban physical form and growth processes (e.g., Arlinghaus 1985; Arlinghaus and Arlinghaus 1989; White and Engelen 1993; Batty and Longley 1994; Frankhauser 1994; Batty and Xie 1996; Wentz 2000; Gomes 2001; Shen 2002).

This paper aims at understanding the spatial internal layout of the city with fractal tools. We know that the city's design emerges on its own in accordance with a locally ordered system (Hillier 1996; Hillier and Hanson 1984). The spatial structure of cities is indeed a disorderly outcome of a long history of small incremental changes that occurred at large scales. The resulting patterns have neither geometrical nor functional simplicity. The metropolitan feature is here limited to the built-up pattern and hence represented by a lattice of residential sites offering urban amenities and, in the interstices, "green areas" (that is to say areas that are not built up), where consumers enjoy "rural" leisure amenities. These empty spaces are ranked following an inverse hierarchical order. This structure breaks the geometry of the nested and specialized rings of the Thunen City. Hence, in order to formalize the urban area, we need a geometry that enables the nesting of residential and rural areas within a nonhomogeneous hierarchically organized pattern, with lacunae and fully occupied cells. Fractal geometry meets these conditions; it is by construction a hierarchical organization of nested objects at different scales (see Cavailhes et al. 2002).

Batty and Longley (1994, chap. 6) have tried to link fractality to the morphology of urban land use in the city of Swindon, England. They limited themselves to the type of land parcels (residential, commercial-industrial, educational, transport and open space). It has also been shown that fractal shapes reduce travel costs to urban sites and green areas, and that peripheries of cities look fractal (Anas, Arnott, and Small 1998; Frankhanser 1998). This paper aims at further analyzing the structure of the intra-urban built-up areas by (1) taking the built-up structure into account, (2) using different fractal measurement methods, and (3) linking the obtained values to variables commonly used in spatial urban economics, urban geography, and land-use planning. The experiment is performed on Brussels, a city where most residential wards were planned by private property developers. …

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