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The spatial organization of metropolises is a complex assembly of physical and functional interactions that shape urban structure over time. Neglecting the dynamics of this structure and its uncoordinated management results in consequences such as urban sprawl. Therefore, a precise analysis of physical expansion trends in cities is vital for formulating sustainable development plans.

The present study aims to analyze the physical structure transformations within the spatial organization of the Mashhad metropolis over the past half-century. The research methodology of this study is descriptive-analytical. The required data and information were gathered through documentary and archival methods, including spatial data from urban block censuses and approved master plan maps. For the physical evaluation, Galster’s eight-dimensional framework was utilized, and data analysis techniques include Shannon's Entropy model, Global Moran's I (Spatial Autocorrelation), and the Standard Deviational Ellipse model. Furthermore, a Geographic Information System (GIS) was employed for data processing and spatial modeling.

The findings indicate that the Shannon Entropy index for Mashhad fluctuated consistently above 7.5 (relative to a maximum natural logarithm of 10) throughout the study period. Specifically, during the first period (1986–1996), due to a physical explosion, the index rose from 8.4 to a peak of 8.8; it decreased to 7.8 in the second decade under a compaction-oriented approach, and rebounded to 8.1 during the third decade with the emergence of a polycentric metropolis