This paper introduces the mechanism of diffusion-limited aggregation (DLA) as a new basis for understanding urban growth. Through DLA, urban form is related to the processes of rural-to-urban migration and contiguous growth. However, despite being based on very simple principles, DLA simulations are shown to have properties found in most urban areas such as negative density gradients and ordered chaotic structures. The paper examines variations in the simulated urban structures produced by different assumptions regarding the rural-to-urban migration mechanism. An important finding is that urban density gradients can occur independently of the generally accepted reasons for their presence. We also comment on boundary effects in the measurement of urban density gradients.
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Fotheringham, A.S., Batty, M. & Longley, P.A. Diffusion-limited aggregation and the fractal nature of urban growth. Papers of the Regional Science Association 67, 55–69 (1989). https://doi.org/10.1007/BF01934667