The fractal simulation of urban structure
This paper is addressed to the problem of developing realistic-looking patterns of land use and activity from predictions generated by conventional urban models. The method developed is based on a geometric model of irregularity involving hierarchical cascading and recursion, whose rationale lies in the emergent field of fractal geometry. First the idea of fractans -- shapes with fractional dimension -- is introduced and then it is shown how two-dimensional patterns whose dimensions are consistent with a large city such as London can be simulated at different levels of detail or recursion. It is then argued that the hierarchical structure of cities should be exploited as a basis for such simulation, and it is argued that discrete choice models of individual spatial behaviour have excellent properties which enable their embedding into such simulations. The standard multinomial logit model is presented and then applied to house-type data in Greater London. A variety of models are estimated, house-type choice being related to age and distance from the centre of the city, and the spatial biases in these predictions are then mapped using prediction success statistics. These models are then used at the base level of a fractal simulation of house type and location in London. Random and deterministic model simulations are developed, and an unusual and possibly innovative feature of these simulations involves the way the inputs and outputs, data and predictions, are simultaneously displayed on the graphics device used. Conclusions for further research, particularly in spatial hierarchical modelling, are then sketched.