Space-time patterns of urban sprawl, a 1D cellular automata and microeconomic approach

We present a theoretical model of residential growth that emphasizes 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 to both like and dislike the density of their neighbourhood, and 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 visualize 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.