Dielectric breakdown and urban growth: Morphological similarities or conceptual links?

Urban dynamics generate sprawl patterns that reveals in many cases fractal-like properties. This is the reason why a couple of research projects focused on how to simulate the growth of such patterns while respecting their fractal features. It is well-known that cellular automata can be used for generating random fractal structures. This holds e.g. for certain models developed in physics like DLA (Diffusion Limited Aggregation) or DBM (Dielectric Breakdown Models) and thus such models inspired urban growth simulation models. However in physics these models are based on a transcription of the underlying physical laws, combining electrodynamics and thermodynamics. Hence DLA and DBM are not just morpho-descriptive, but refer to explanatory approaches. However it seems difficult to establish a direct causal link between these approaches and urban growth.
The goal of several recent models was to introduce a more explanatory approach for simulating the emergence of urban patterns by means of cellular automata. Following this objective, micro-economic reasoning has been used for describing households’ residential choice behaviour and constituting the driving force of cellular automata. These models assume that households settle down subsequently in the vicinity of a preexisting CBD where jobs are localized. Households have preferences for social and green amenities in their neighbourhood. Even if these approaches can explain some properties of urban growth processes, like leapfrogging, the patterns generated do not really show fractal properties, even if some morphological analogies with DBM have been identified. Moreover in the enunciated models, the dynamics is driven only by the evaluation of households who to want to settle down in the already existing city region. The City Administration is supposed to construct new road segments without consequences for the budget of the households. This is questionable. Here we introduce a model that starts from a pre-existing cross-like street network with a CBD at the crossing point where all kinds of services, shopping amenities and jobs are concentrated. However we introduce a series of new mechanisms. First, new arriving households use the utility of already located households as a reference. Second a tax per household is introduced for maintaining the existing street network and the infrastructures of the pre-existing centre. New households can improve the utility of urban population by contributing to these fixed costs. However if a well evaluated site needs to be connected by a new road segment to the existing street network, this will increase the costs for total maintenance of the street network and thus the tax. Third, each household wants to benefit from green amenities for different use (daily walks, playground, hiking…) but the construction of side branches of the road network can impede direct accesses to open landscapes and can generate supplementary travel costs thus impacting the budget of households. This “shadowing effect” reminds some mechanisms of the DBM-models. The model thus combines different aspects acting positively or negatively on the households’ utility and budget. According to the expected changes to their indirect utility function, the households who have settled down earlier in the city will not be in favour of accepting new households. This paper focuses on the conceptualization of the model and on the morphological properties of the emerging patterns. It is illustrated by several simulation results.