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This paper couples a Forward Feature Selection algorithm with Random Forest (FFS-RF) to create a transition index map, which then guides the spatial allocation for the extrapolation of urban growth using a Cellular Automata model. We used Landsat imagery to generate land cover maps at the years 1998, 2008, and 2018 for the Tehran-Karaj Region (TKR) in Iran. The FFS-RF considered the independent variables of slope, altitude, and distances from urban, crop, greenery, barren, and roads. The FFS-RF revealed temporal non-stationary of drivers from 1998–2008 to 2008–2018. The FFS-RF detected that altitude and distance from greenery were the most important drivers of urban growth during 1998–2008, then distances from crop and barren were the most important drivers during 2008–2018. We used the Total Operating Characteristic to evaluate the transition index maps. Validation during 2008–2018 showed that FFS-RF produced a transition index map that had predictive power no better than an allocation of urban growth near existing urban. Simulation to 2060 extrapolated that Tehran, Karaj, and their adjacent cities will interconnect spatially to form a gigantic city-region. [Display omitted] • A Forward Feature Selection - Random Forest (FFS-RF) model describes urban growth. • FFS-RF found temporal non-stationarity of drivers in Iran's Tehran-Karaj region. • The Total Operating Characteristic evaluated the transition index map (TIM). • FFS-RF produced a TIM that has predictive power no better than a baseline TIM. • FFS-RF and Cellular Automata extrapolated urban growth to the year 2060. [ABSTRACT FROM AUTHOR]