Monocentric urban simulation models: getting closer to fractal properties and landscape representation

Urban growth generates spatial patterns that in many cases demonstrate fractal properties. Geocomputational models, particularly cellular automata and spatial agent-based simulation models have been used over the last 20 years to generate urbanisation patterns with the aim to replicate at best observed expansion footprints, including matching observed and simulated fractal dimensions. In applied cases, with the addition of constraints at multiple scales (land constraints, threshold per zones, etc.) simulation models seem to perform rather well and obtain sound urban fractal dimensions. Models that are more parsimonious in parameters however do not seem to perform as well. Exceptions are those models directly inspired from physics such as DLA (Diffusion Limited Aggregation) or DBM (Dielectric Breakdown Models) but these are frustrating when it comes to behavioural or economic interpretation. Models with explicit micro-economic component in a monocentric setting also seem to lag behind in terms of fractal performance: unless exogenous spatial heterogeneity is provided, the spatial outcome of these models is too homogenous to resemble real cities, despite agglomeration and dispersion processes at neighbourhood scale and despite the self-emergence of road networks and subsequent open land lock-ins.

Rather than resolving to exogenous polycentric setting or exogenous stochasticity that would provide better looking outcomes, we investigate this insatisfaction by exploring the results of an augmented micro-economic simulation model on a theoretical monocentric space. The innovations are brought along three rationales:

Firstly, an assumption is made that the length of the infrastructure network should feed back into households budget. Cities cannot expand too quickly not only because of unitary commuting costs but also infrastructure costs. We therefore implement an infrastructure tax that should lead to agglomeration or a more efficient generation of roads from the city perspective.

Secondly, we assume that the infill of undeveloped spaces by new residents is limited by residents who settled earlier in the city and refuse important utility losses in terms of open green space. This leads to relaxing the assumption of a dynamic adaptation of rents and building stock trough time. Free entry and placement is somehow limited by a public authority that keeps utility at its higher possible state at each time step.

Thirdly, we abandon the assumption that neighbourhood quality is related to the density of available activities or the density of green space within a given neighbourhood, but replace this with the access to a diversity of urban and green opportunities depending on their use frequency (daily walk, playground, hiking in forest,…). This is a very important change in geocomputational terms since simple focal functions can no longer be used to represent externalities in simulation models. The gradual construction of roads and houses change gradually the nature of the landscape and the value taken out of it, typically by dividing green patches into parts, creating detours to access bigger parks, shadowing effects, etc. In addition, this requires that landscape objects are represented as vectors, not cells, which is a second important change in geocomputational terms. To some extent this brings urban simulation models closer to landscape ecology and graph-based approaches.

In this paper we explore and contrast the effects of the three mechanisms mentioned above on the resulting urban morphology.