Fractal Analysis of Digital Data

Paul Longley
Department of Geography, University of Bristol, University Road, Bristol BS8 1SS, United Kingdom

Abstract
This paper will review some of the achievements and limitations of the "fractal cities" project (Batty & Longley, 1994), and will identify some aspects of other GIS-based projects which have implications for the ways in which digital geographical data may be assembled and used in fractal analysis.

The first part of the presentation will consider some of the ways in which fractal geometry, through the medium of computer graphics, has been used to reinvigorate analogue model-building in geography. In particular, we will review the development of models based upon diffusion-limited aggregation and dielectric breakdown to simulate the processes of urban growth and the evolution of density gradients in cities. Early (mid 1980s) work which sought to re-establish linkages between the form of cities and the changing processes which govern spatial growth will also be reviewed. Research in this vein became possible in the 1980s because of the innovation of computer graphics, and because ongoing reductions in the cost of computer power have made it possible to calculate reliable statistics of shape and form in a routine manner. However, as elsewhere in scientific visualization, computational short-cuts will continue to be of importance in the fractal simulation of urban structure.

Much analogue and other simulation modelling is founded upon the premise that computation is a necessary substitute for adequate information about the real world. Given the current proliferation of digital databases, the realm of analogue modelling looks set increasingly to become an historical one. In the second part of this paper, we will assess some of the implications of the data processing revolution for the analysis of urban structure. First, we will conduct a retrospective interpretation of a morphometric analysis of settlements in the South East England green-belt, and will suggest some ways in which the nature and quality of early 1990s digital data prescribed the results of a regional analysis. Second, drawing upon work carried out in Bristol by Victor Mesev and others, we will assess some of the technical and methodological problems inherent in the integration of diverse datasets. In so doing, we will pay particular attention to the problems encountered in integration of socio-economic datasets with satellite imagery, and will suggest ways in which integrated 'RS-GIS' datasets permit calculation of a wider and richer range of urban morphological measures. Third, we will return to our earlier analogue models, in order to re-evaluate thinking about urban density gradients in the light of recent analysis using 'RS-GIS' datasets.

In conclusion, and in contrast to the suggestions of detractors of GIS, we will review a number of ways in which 'geocomputation' has pushed forward geographical analysis and understanding. We will identify some ways in which geographical model-building should respond to the digital data revolution in order to create ever more realistic and data-rich portraits of reality. Finally, we will reflect that while fractal geometry helps us to see many things differently, it also changes our perceptions concerning the certainty of 'reality' and how we might manipulate it: we conclude with some speculations as to how, in this context, we might respond to the challenge of linking the physical form of cities to the social, economic, and institutional processes which are central to their functioning.

References
Batty, M. and Longley, P. 1994. Fractal Cities: a Geometry of Form and Function. London and San Diego: Academic Press.