Analysis of urban sprawl dynamics using machine learning, CA-Markov chain, and the Shannon entropy model: a case study in Mbombela City, South Africa

Over half of the world’s population resides in urban areas. We anticipate that this pattern will become more evident, notably in South Africa. Therefore, research on urban spirals, both past and projected, is necessary for efficient urban land use planning and management. This study aims to assess the spatio-temporal urban sprawl dynamics from 2003 to 2033 in Mbombela, South Africa. We employed robust approaches such as machine learning, the cellular automata-Markov chain, and the Shannon entropy model to look at how urban sprawl changes over time using both the Landsat 4–5 Thematic Mapper and the 8 Operational Land Imagers. We conducted this study to bridge the gaps in existing research, which primarily focuses on past and current urban growth trends rather than future trends. The findings indicated that the coverage of built-up areas and vegetation has expanded by 1.98 km2 and 13.23 km2 between the years 2003 and 2023. On the other hand, the amount of land continues to decrease by -12.56 km2 and − 2.65 km2 annually, respectively. We anticipate an increase in the built-up area and vegetation to a total of 7.60 km2 and 0.57 km2, respectively, by the year 2033. We anticipate a total annual decline of -7.78 km2 and − 0.39 km2 in water bodies and open land coverage, respectively. This work has the potential to assist planners and policymakers in improving sustainable urban land-use planning.