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Restricted by urban development stages, natural conditions, urban form and structure, diffusional growth occupies a large proportion of area in many cities. Traditional cellular automata (CA) has been widely applied in urban growth studies because it can simulate complex system evolution with simple rules. However, due to the limitation of neighborhood conditions, it is insufficient for simulating urban diffusional growth process. A maximum entropy mode was used to estimate three layers of probability spaces: the probability layer of cell transformation from non-urban status to urban status (PLCT), the probability layer for aggregated growth (PLAP), and the probability layer for diffusional growth (PLOP). At the same time, a maxent category selected CA model (MaxEnt-CSCA) was designed to simulate aggregated and diffusional urban expansion processes simultaneously. Luoyang City, with a large proportion of diffusional urban expansion (65.29% in 2009–2018), was used to test the effectiveness of MaxEnt-CSCA. The results showed that: (1) MaxEnt-CSCA accurately simulated aggregated growth of 47.40% and diffusional growth of 37.13% in Luoyang from 2009 to 2018, and the overall Kappa coefficient was 0.78; (2) The prediction results for 2035 showed that future urban expansion will mainly take place in Luolong District and the counties around the main urban area, and the distribution pattern of Luolong District will change from the relative diffusion state to the aggregation stage. This paper also discusses the applicable areas of MaxEnt-CSCA and illustrates the importance of selecting an appropriate urban expansion model in a region with a large amount of diffusional growth.

Urban Land Expansion Simulation Considering the Diffusional and Aggregated Growth Simultaneously: A Case Study of Luoyang City