Abstract. Understanding Built-up evolution and complexity over time is attained to exercise sustainable development and smart implementations in the future. The Spatiotemporal evolution of built-up analysis is carried out using the centroid shift model considering the geometry of the built-up from 1975 to 2019 (1975, 1990, 1999, 2009, and 2019). The centroid shift indicates the trajectory of the growth pattern and the future direction of growth. The study area experienced a unidirectional growth pattern till 2009, considering 1975 as the base year, and by 2019 the growth direction shifted by 3.52 degrees, and the overall centroid shift magnitude was 2.42 km2. The non-Euclidean geometric nature of the physical world puts forward fractal geometry to understand the complexity of built-up. The mean fractal dimension index shows the growth type in the study area; a directional approach towards the mean fractal dimension provides a critical understanding of the complexity around the built-up Centroid. Among all the eight directions considered, NW_W showed maximum built-up growth with infilling growth type, and the E_SE direction showed a significant jump in an area with external expansion by 2019. This direction indicates the future growth direction. The study concludes that complexity analysis critically enhances the spatiotemporal dynamics of built-up evolution.