Space–Time Patterns of Urban Sprawl, a 1D Cellular Automata and Microeconomic Approach

We present a theoretical model of residential growth that emphasises the path-dependent nature of urban sprawl patterns. The model is founded on the monocentric urban economic model and uses a cellular automata (CA) approach to introduce endogenous neighbourhood effects. Households are assumed both to like and to dislike the density of their neighbourhood, and are assumed to trade-off this density with housing space consumption and commuting costs. Discontinuous spatial patterns emerge from that trade-off, with the size of suburban clusters varying with time and distance to the centre. We use space–time diagrams inspired from 1D elementary CA to visualise changes in spatial patterns through time and space, and undertake sensitivity analyses to show how the pattern and timing of sprawl are affected by neighbourhood preferences, income level, commuting costs, or by imposing a green belt.